first of all, i thought i'd list deadpool's most prized possessions: a picture of him and syrin, Kinpin's stolen underwear, a Yoda doll stolen from Mark Hamill, blind al's ulcer pills, amelia earhardt's pilots licensce, dr. doom's mask.
anyway, #1 reason he woudn't be an avenger-he likes making prank calls, and in one of the issues he first prank calls wolverine (whatever the question was, wolverine replies "i make sure they're fully retracted before i go"😉 and then captain america. apparently cap didn't really think it was in good taste to be asked if he had "Bucky in a can". so yeah, pissin off cap isn't a good start.
funeral for a freak was the funniest comic story i've ever read. and the comic you speak of is a mini series called identity disc. i don't know if DP's involved but bullseye and the juggernaut definitly are. basically some villian threatens to kill their loved ones unless they band together and find a disc that AIM has with every hero's secret identity (i wasn't actually aware that bulls had any loved ones. i figure he's in it just to kill people and get money).