They're in no particular order. If I had a six-slot and wanted to pick six games for it, they would probably be:
Metal Slug
Metal Slug 3 or Shock Troopers
Last Blade 2
SS V Special (replace with SSII or IV if V is too expensive for your tastes)
Garou : MOTW
and either Neo Turf Masters, Baseball Stars 2, or Magical Drop 3.
However, keep in mind that I'm a huge Metal Slug fan (1st one is my favorite game ever), and I don't care for most puzzlers too much. I also would pick Shock Troopers (Commando-style game) over any of the traditional shmups on the console. The console has some good shmups (in addition to Pulstar, Blazing Star, and Viewpoint, you also have Strikers 1945+, Aero Fighters 2 and 3, and Prehistoric Isle 2, which are all pretty good, along with a few other decent ones), but in my opinion the Neo's shmups, even the good ones, are totally overshadowed by shmups on other systems, whereas the Metal Slug games and many of the system's fighters are hard to top.
I've also omitted any KOF games from the above list, just because I prefer the weapons-based games and Fatal Fury to KOF, but many people feel differently, and you need to own at least one KOF game if you have a Neo. Opinions vary widely on which games are the best, but '98 is cheap and widely regarded as one of the best. I also like 2k1-2k3 a lot, but be warned that the artwork in 2k1 and 2k2 is kind of weak (although the gameplay in both games is good).
edit - also, opinion on best Slug game varies quite a bit as well. I think the original is the best by a fair margin, but it is also the easiest. 3 has the most set-pieces and variety, and X has a good balance. Don't get 2 -- it's just like X, and better than it in some ways (color schemes), but it has severe slowdown in 2p mode that X doesn't have. 4 and 5 aren't really worth it on MVS in my opinion (although by all means get the PS2 double pack).
