I am huge fan of TMNT and the games, and my personal picks are :
TMNT 3 on NES
Hyperstone on MD
Tournament Fighters on MD
Shredder's Revenge
I have not played extensively every single game, but most of the major, older games though.
Never was a fan of the first on NES, I don't find that it aged that well. TMNT2 is awfully difficult and cheap. TMNT 3 (which I still own my original copy) however is excellent, well balanced, has a ton of content and is super fun.
Played only the first one on GB and it was very well made ! The third one is a kind of Metroid like game I think.
Both arcade games are pretty but the hitboxes are awful and they are very cheap as well, made to have you spend credits. I don't find them very fun to come back to. TMNT IV on SNES was a good improvement on the arcade game, with tighter controls, a lot of content, but still I don't find it as satisfying as Hyperstone. Hyperstone is short on content but the gameplay is the best and it plays like a dream. It's too easy though.
I have played all Tournament Fighters games and they are all fine for their respective consoles, my preference going to the MD game. I think that it plays well, it is fast, high resolution, some stages have two levels, and there is a nice hack available out there to unlock all three bosses. A case of a fighting game that was specifically designed for the MD, rather than being a port or a multiplatform game suffering from the lower resolution of the SNES counterpart (which happened way too often).
Shredder's Revenge is a lot of fun, highly recommended. Awesome soundtrack as well by Tee Lopes.