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.