A small confession: I am much more attached to the Rankin Bass Gollum than I am to the Weta version. Don't get me wrong, Andy Serkis did a stand-up job and the animation was groundbreaking and it makes a lot more sense in the long run, but come on. What's more interesting to look at? This guy or this guy? Those Rankin Bass guys were out of their minds on a lot their designs, but their Gollum is hilarious and great.
Anyway, Gollum is described as being slimy and dark as darkness, with long thin fingers, big lamp-like eyes and six teeth. He has pockets or at some point in the past has pockets.There are only small allusions to Gollum living outside of the cave and even smaller ones to him previously being a hobbit. I've been thinking a lot about all of the weird versions of Gollum that have cropped up over the years (a bunch compiled by Carson Ellis here), though many of those don't make a lot of sense in my version. I don't think Gollum can be be much bigger than Bilbo, if he has to resort to throttling goblins from the shadows to kill them. I picture him a lot like the corpse of a frog man, or like some little crustacean always between shells.
Only a few of these are alright, but they are a good starting point.