If you are only going to have one, go AM for sure. With a budget of $1000, stick with a hardtail, unless you want to do gobs of research before finding a lucky deal on a used FS. With a budget of $1600, a few FS bikes become worth considering (Kona Dawgs and Coilers come to mind). Up that to $2500, then really good FS bikes come into play. Sky's the limit from there, really.
Generally speaking, a HT is going to allow for much more versatility in a single bike. If it was me, I'd look to get something like a Banshee Scirocco, SC Chamelion, or a Sinister Ridge - each with a Pike. You'd have to get a good deal on the frame since both the Banshee and the Sinister retail at around $700. (and good deals are to be found).
I started in exactly your position and it took me forever to find the right bike. I went from thinking $1500 would get me what I want to the realisation that I would have to spend WAY more thatn that. In the end I got EXACTLY what I was after (Sinister Splinter MX) and now I could not be happier with my decision.