A lot of the classics are great on the Neo Geo to me, but some aged rather poorly. Some of the well known ones as mentioned, including Fatal Fury 1 are still enjoyable. I still think Fatal Fury 1 is an important entry out of the fighting games on the Neo, even though it's dated and the controls are sluggish.
My personal favorites, roughly are:
Nam 1975
Last Resort
Fatal Fury 1 and Special
Baseball Stars 2
Samurai Shodown 2
KOF 95/96/97 (I like the story scenes and overall presentation, what can I say.)
Art of Fighting 3
Last Blade 1
Shock Troopers 1
Real Bout Fatal Fury Special and Real Bout 2 (It is a tie with these two. RBS would be the best to mention though)
Metal Slug 3 (Say what you will about it being long, but this one just had the most action and fun to me. I like 1, 2, X and 3)
Mark of The Wolves
Notice I don't mention Playmore released titles, :-" . Yep, didn't really like the new SNK after 2000 that much. Even though, most of the games I don't like from then on, I feel that Rage of The Dragons, KOF 2002 and Matrimelee are pretty decent games. Still, they just don't compare to the original SNK company made games to me.
A good way to go about it would be to pick 1 of each category out of the classics, and 1 of each category out of later releases from maybe 1996-200X. The games changed a lot in the mid-late 90s compared to the games released in the first couple of years. We went from classic arcade to more of in depth and slightly more complicated arcade games. Similar to the transition of arcade games ported on the Genesis and then to the Saturn.
Keep in mind that each fighting game series to me, is a different category when it comes to the Neo Geo. So you got Art of Fighting, Fatal Fury, Samurai Shodown, KOF, Last Blade, World Heroes and Savage Reign even. Then there are the single titles like Gowcaizer, Mark of The Wolves, Rage of The Dragons, etc... I guess, just pick favorites out of each series and then a few single titles that are most liked when it comes to fighting games.
A good list to use would be:
Nam 1975
Magician Lord
Super Sidekicks 1-3 - pick which one
Baseball Stars 1 or 2
Last Resort
King of The Monsters 1 or 2
Sengoku 1 or 2
Fatal Fury 1
AOF 1 or 2
Samurai Shodown 1 or 2
Top Hunter or Spinmaster
KOF 94 and 98
Magical Drop or Puzzle Bobble games - pick which one
Metal Slug 1, 2, X or 3
Shock Troopers 1
World Heroes 1 or 2
Ninja Masters
Last Blade 1
Real Bout Special
Mark of The Wolves
This is just a rough list I would go by. I don't know too much about the puzzle, racing and sports games all that much. I only own a few from each of those categories, but not one puzzle game for some reason.