
I generally collect in this order of priority:
1. Genre - I've restricted myself to mainly trying to acquire artwork from anime that were based off ren'ai (romantic love) games. For example right now I'm trying to get artwork from (among others):
AIR
Akane Maniax
Ar Tonelico OVA
Campus
Canvas
Canvas 2
DNAngel
Doukyuusei (English title = "End of Summer")
Doukyuusei Climax Files
Doukyuusei 2
Escalayer
Futakoi Alternative
Guren (Crimson Lotus/English title = "Blood Shadow")
Iriya no Sora
Kakyuusei (TV or Elf ban)
Kanon
Kimi ga Nozomu Eien
Koihime
Mizuiro 1st or 2nd OVA
Natsuiro no Sunadokei ("Hourglass of Summer")
ONE 1st or 2nd OVA
Refrain Blue
Sadamitsu
Sentimental Journey
Shingetsutan Tsukihime
Shuffle!
Sister Princess RePure
Suika (English title = "Wet Summer Days")
Tenkousei
To Heart
To Heart 2
Tokimeki Memorial
Wind ~ a Breath of Heart (TV or OVA, but preferably TV)
2. Anime Title
3a. Character - I'm very character centered. I'm not a "collect-all-the-characters" person except when it comes to the thirteen female characters of the Elf Kakyuusei anime.
3b. Character in a memorable scene.
To summarize, I generally go after either:
1. Good character artwork from a genre anime that I like or...
2. Nice scene artwork with a character that I like in it.
I rarely buy artwork without characters in it that I like. I rarely buy artwork from anime I don't like. I'm less likely to buy artwork from a scene I don't remember and I'm more likely to buy artwork from something that elicits an emotional reaction out of me when I think back on it.

EDIT:
Oh yeah...I forgot something important. The artwork I get almost HAS to have a female character in it. lol
