Final Fantasy Adventure is the best Mana-series game ever and always has been. It's a fantastic classic with heavily Zelda-inspired combat, but in an action-RPG with a levelling system and such. I love the simple combat, it's by far my favorite in the franchise. The story is relentlessly depressing, also. The graphics are average stuff, but I love the soundtrack -- it's one of my favorite chiptune soundtracks. The main theme, Rising Sun, is pretty amazing and has the exactly right tone for such a tragedy-heavy game. FFA (or Mystic Quest, or whatever you call it) is an amazing classic that holds up fairly well, so long as you make sure to always keep plenty of keys and mattocks and look up a few of the tougher puzzles it's a must-play as far as I'm concerned!
Secret of Mana is a good game, I guess, but I've always had a lot of issues with it. First, the combat feels AWFUL. There is a long delay on every hit, and it feels terrible every time! And on top of that, they put in a charge system on attacks, so you need to wait quite a while between attacks in order to hit at full strength. I've always quite disliked this system. Additionally, this is a much more linear and straightforward game than FFA is; you will never get lost, because you never really have to think about where to go, just follow the obvious plot path and you'll be fine. I have no problem with games being linear, but it does feel like this one loses a bit for it. Additionally, and in this release you can use savestates so the problem is mostly averted, but in its original form, FFA has save anywhere. Secret, however, does not; you can only save at save points... and this matters a lot, because the game is VERY grindey at times. I can't even count the number of times I reached a boss, only to find I was way too low level, die, and have to go back to my last save, grind, and then try the guy again later. I really dislike that kind of game design. This collection's savestate functions help a lot, but it's still not that great; I've long considered Secret of Mana good but over-rated and not really my thing. Oh, the graphics and music are good, but I find FFA's music much more memorable, though nostalgia for it may be part of that. The story is less interesting as well, for me anyway.
Trials of Mana, the third game, is a fantastic game that I highly recommend in its original form. Fixing almost all of the problems of Secret of Mana's combat system, Trials gets rid of the horrible attack delay. Sure, it still has a mostly linear world (within each of the six characters' stories) and has the charge meter system, but retuning things to get rid of that awful delay works wonders, and Trials feels good to play. I like the six characters to choose from too, it gives you more options than the previous two. It's a great game and one of the better action-RPGs that gen. You could wait for the remake, but none of the FFA remakes (Sword of Mana, the Vita/phone remake of the original, etc.) are as good as the original in my opinion, and the Secret of Mana's remake is pretty flawed too. The Trials remake is looking better, but I still am not going to assume it'll be better than the original.
So yeah, play FFA and Trials, maybe skip most of Secret. Try a bit of it and see if you can tolerate the combat...