If you don't have a strong emotional connection to Fats - and I suspect that because you're asking you don't - I'd probably leave them alone. With precious few exceptions, old mountain bikes are really bad investments.
Apart from real fringe models, Yo Eddys/Titaniums w/steel forks are the most available collectible models it would seem. Earlier bikes don't command much attention or high dollar.
There are a few fringe bikes - 10th Anniversary, track and the Chris Cross - that are nearly unobtainable and - at least until cross recedes back into the muddy hole it has crawled out of in the past 5 years - probably gold standard Fats.
Trials, True Temper Kickers with unicrowns and weird one-offs always seem to me to be given away to good homes.
I don't believe that anyone actually sets out to buy a Buck Shaver or Bro Eddy. Betty's - not trying to be sexist - but there's only so many guys with sympathetic partners.
Wickeds, Teams and old race bikes seem to be more variable. They don't command high dollar though... 2/3s at most of a Yo.
I'd be looking at early bikes - Fat Mike NYC has tremendous examples - 531 frames, box crowns if I were getting into it now. These would be a shock to ride for most people familiar with modern mountain bikes (too short on the top tube, too little stand-over, too long chainstays, too slack head tube, kinda porky, too little brakes, etc.). Aesthetically and emotionally though, for me, they are tits.
Know that a full restore will be in the $2-$3K zone and worth about a half (Wickeds, Teams, Road bikes) to two-thirds (Yos) that when completed to a very, very high standard (basically NOS). Decals are tough if you're a stickler with a weird model.
Generally, we're a pretty mellow bunch here. Tell us what you're considering, how much, with some photos of condition and you'll get good feedback.
Thanks for the great info guys. I am looking to spend around $800 or less if possible. I am looking for an 18-19 1/2 size frame that is in overall good condition. I have been looking on ebay and craigslist and ebay has high prices and everything seems to go quickly on craigslist, any thoughts about where else I should look to find a good price?
I was wondering if you guys think I would fit a 19.5 inch frame considering I am 5"9?