With the following command you can obtain a list of installed packages, classified by priority:

dpkg-query -Wf '${Package;-40}${Priority}

' | sort -b -k2,2 -k1,1

A description of priorities is given in the Debian Policy Manual.

In my installation I obtain the following (I only show required, important and standard packages):

apt                                     important

aptitude                                important

apt-utils                               important

bsdmainutils                            important

cron                                    important

debconf-i18n                            important

dmidecode                               important

gnupg                                   important

gpgv                                    important

groff-base                              important

info                                    important

install-info                            important

iptables                                important

iputils-ping                            important

isc-dhcp-client                         important

isc-dhcp-common                         important

libapt-inst1.3                          important

libapt-pkg4.11                          important

libboost-iostreams1.46.1                important

libcwidget3                             important

libept1                                 important

libgdbm3                                important

libgdbm3                                important

libgudev-1.0-0                          important

libnewt0.52                             important

libpcre3                                important

libpipeline1                            important

libpopt0                                important

libreadline6                            important

libssl1.0.0                             important

libsysfs2                               important

libusb-0.1-4                            important

libxapian22                             important

logrotate                               important

man-db                                  important

manpages                                important

medibuntu-keyring                       important

nano                                    important

netbase                                 important

net-tools                               important

python                                  important

readline-common                         important

rsyslog                                 important

ubuntu-extras-keyring                   important

ubuntu-keyring                          important

vim-common                              important

vim-tiny                                important

wget                                    important

whiptail                                important

adduser                                 required

base-files                              required

base-passwd                             required

bash                                    required

bsdutils                                required

busybox-initramfs                       required

coreutils                               required

cpio                                    required

dash                                    required

debconf                                 required

debianutils                             required

diffutils                               required

dpkg                                    required

e2fslibs                                required

e2fsprogs                               required

findutils                               required

gcc-4.6-base                            required

gcc-4.6-base                            required

grep                                    required

gzip                                    required

hostname                                required

ifupdown                                required

initscripts                             required

insserv                                 required

iproute                                 required

klibc-utils                             required

libacl1                                 required

libacl1                                 required

libattr1                                required

libattr1                                required

libblkid1                               required

libbz2-1.0                              required

libc6                                   required

libc6                                   required

libc-bin                                required

libcomerr2                              required

libcomerr2                              required

libdb5.1                                required

libdbus-1-3                             required

libdevmapper1.02.1                      required

libdrm2                                 required

libdrm-intel1                           required

libdrm-nouveau1a                        required

libdrm-radeon1                          required

libffi6                                 required

libgcc1                                 required

libgcc1                                 required

libglib2.0-0                            required

libklibc                                required

liblocale-gettext-perl                  required

liblzma2                                required

libmount1                               required

libncurses5                             required

libncursesw5                            required

libnih1                                 required

libnih-dbus1                            required

libpam0g                                required

libpam-modules                          required

libpam-modules-bin                      required

libpam-runtime                          required

libpciaccess0                           required

libpcre3                                required

libplymouth2                            required

libpng12-0                              required

libselinux1                             required

libselinux1                             required

libslang2                               required

libss2                                  required

libssl1.0.0                             required

libstdc++6                              required

libstdc++6                              required

libtext-charwidth-perl                  required

libtext-iconv-perl                      required

libtext-wrapi18n-perl                   required

libtinfo5                               required

libudev0                                required

libuuid1                                required

libuuid1                                required

locales                                 required

login                                   required

lsb-base                                required

lzma                                    required

makedev                                 required

mawk                                    required

module-init-tools                       required

mount                                   required

mountall                                required

multiarch-support                       required

ncurses-base                            required

ncurses-bin                             required

passwd                                  required

perl-base                               required

plymouth                                required

procps                                  required

python2.7-minimal                       required

python-minimal                          required

sed                                     required

sensible-utils                          required

sysvinit-utils                          required

sysv-rc                                 required

tar                                     required

tzdata                                  required

udev                                    required

upstart                                 required

ureadahead                              required

util-linux                              required

xz-utils                                required

zlib1g                                  required

zlib1g                                  required

at                                      standard

bash-completion                         standard

bc                                      standard

bind9-host                              standard

dc                                      standard

dnsutils                                standard

file                                    standard

ftp                                     standard

gettext-base                            standard

less                                    standard

libbind9-60                             standard

libcap2                                 standard

libdb5.1                                standard

libdns69                                standard

libedit2                                standard

libevent-2.0-5                          standard

libgc1c2                                standard

libgcrypt11                             standard

libgcrypt11                             standard

libgnutls26                             standard

libgnutls26                             standard

libgpg-error0                           standard

libgpg-error0                           standard

libgpm2                                 standard

libgssapi-krb5-2                        standard

libgssapi-krb5-2                        standard

libidn11                                standard

libidn11                                standard

libisc62                                standard

libk5crypto3                            standard

libk5crypto3                            standard

libkeyutils1                            standard

libkeyutils1                            standard

libkrb5-3                               standard

libkrb5-3                               standard

libkrb5support0                         standard

libkrb5support0                         standard

libldap-2.4-2                           standard

libldap-2.4-2                           standard

liblockfile1                            standard

liblwres60                              standard

libmagic1                               standard

libpci3                                 standard

libsasl2-2                              standard

libsasl2-2                              standard

libsqlite3-0                            standard

libsqlite3-0                            standard

libtasn1-3                              standard

libtasn1-3                              standard

libxml2                                 standard

lsof                                    standard

m4                                      standard

make                                    standard

mime-support                            standard

mlocate                                 standard

openssh-client                          standard

patch                                   standard

pciutils                                standard

perl                                    standard

perl-modules                            standard

python-apt                              standard

python-central                          standard

telnet                                  standard

time                                    standard

ucf                                     standard

wamerican                               standard

whois                                   standard

The Base System is defined as a system containing only required and important packages.

Packages marked as standard are not strictly needed for a working system, but you can get into difficulties if you miss them.

So, to remove all unneeded packages (optional and extra), you can execute the following command:

sudo apt-get --simulate purge $(dpkg-query -Wf '${Package;-40}${Priority}

' | 

    awk '$2 ~ /optional|extra/ { print $1 }')

I added the --simulate option to be safe and see what apt says.

Strangely, it asks to remove also some required packages: e2fsprogs, util-linux, hostname and upstart, so it is necessary to reinstall these packages. I would download the packages in advance (apt-get download <packages>), to avoid network problems after.

Take also into account that for a working Wifi you can need some optional or extra package, removed in the above procedure.