After a bit of searching, I found the solution myself:

First, I had to give myself the ownership over /dev/sda4, and I had to give group and others read and execute permission. I did that by changing the partition entry in /etc/fstab.

To do that, I had to know my uid and gid. So the first thing I did was writing the following command in a Terminal:

id $USER

This will give an output like this:

UID=1000(myname) GID=1000(myname) groups=1000(myname),4(adm),24(cdrom), ...

So now I knew that both my uid and my gid were 1000.

Do you already know the name of the NTFS partition? If not, type this command in a Terminal:

sudo blkid

and write down the NTFS partition on a piece of paper.

Now, to change the permissions, I edited /etc/fstab with the nano text editor. So, the next command you have to type in a terminal is:

sudo nano /etc/fstab

Go all the way down and type this line:

/dev/sda4 /media/Data ntfs defaults,umask=0022,uid=YourUIDHere,gid=YourGIDHere 0 0

(You should replace /dev/sda4 by the NTFS partition that you wrote down earlier).

_{Explanation: umask=0022 sets the directory's (d) permissions permissions to drwxr-xr-x, to make sure that the user (me) can read, write and execute (rwx) while the group and others can only read and execute (r-x) the directory, which is what I wanted.}

After that, I could mark the three checkboxes without any errors, and the folder would be shared over the network. Because I was not sure whether the sharing settings would be kept after a restart, I unchecked the checkboxes and added some lines in /etc/samba/smb.conf instead. I did that this way:

In a terminal, I typed sudo nano /etc/samba/smb.conf

I scrolled down to the last line, and pasted the following there:

[MyShare]

    comment = My Share

    path = /media/Data/FolderToBeShared

    browseable = yes

    guest ok = yes

    read only = yes

    create mask = 0755

I saved the file, and then rebooted. The folder was accessible from the network now.