This is a rather open ended question so it is likely to be closed(by the mods, not by me), but to answer your question in a general sense before they do....

HP printers have a good reputation for working with linux.

I am currently using an HP2050 all-in-one and it work flawlessly with 12.04 worked with 11.10 and 11.04.

As far as the ink, that is rather subjective and depends on how much printing you do, I don't do a whole lot. I can only say that it is much better on ink than my Lexmark all-in-one(which didn't work with Linux at all). The ink is about;

Black: $18 for the regular $30 for the high yield(they call it XXL, if I remember right
Color: $25 and $35 I believe, I have not had to buy color ink yet but I did look at it when buying black.

These were the ink prices at my local Dept. store, not sure online but likely cheaper by 20% or more....

I did research to find compatible printers when I needed one and found that most people recommended HP as the most compatible. I bought my HP for under $50 if I remember right.

I did a quick search on www.ubuntuforums.org and found this question, it is about 12.04 but still HP is the most recommended

Which (cheaper) printers work with ubuntu 12.4

Finally, in the post I linked to this link was included, I did a quick check of it and it will allow you to search by Manufacturer and or model # and will tell you how well it works with linux..... http://www.openprinting.org/printers