If you have money, then NeoGeo is awesome (myself, I only get to play it at local laundromats), but if you haven't explored the huge library of Genesis games then I'd definitely go for good old Genny. While some titles are fetching higher prices, a majority of great games can be obtained for a relatively low price (especially if you don't care about condition / inclusion of boxes and manuals).
I think the Genny library is broad enough to offer you more games in the categories you are interested in than the other systems. Well, when it comes to (action) puzzle games, I don't think any library rivals that of NES / Gameboy (folks, tell me if I'm wrong here).
I've never met anyone who was disappointed by Dreamcast (unless they were temporarily soured by buying a crappy game upon its release... but even then they eventually regained their love for DC). I am not familar with its entire library, but I've played many gems.
NOTE: I am totally biased towards 16-bit consoles. Totally.