Personally, I tend towards a team of Crono, Magus and Ayla, especially in the New Game/Continue+. Crono and Magus are basically one another, but switched around. Crono has amazing attack power and speed, and his magic isn't all that shabby either. Magus, on the other hand, isn't anywhere near as great as Crono physically, and even with the considerable damage his scythes do, he just can't match up to Crono, especially when Crono gets his ultimate weapon. As for Magus' magic, though... I've got him doing about twice as much damage magically as Crono, and even able to outdo Lucca in terms of how efficiently they're blown away. He may not be much of a help when it comes to just whacking enemies with a physical attack, but he can lay waste to hordes of enemies with his magic. Both Crono and Magus are fast, so they can toss in an item whenever it's deemed necessary; that's the only reason I survived Queen Zeal my first time around, because I almost always had someone available to use a megaelixir when Zeal started using the 1HP moves on me like crazy.
As for Ayla, I think she's just amazing. She does just about as much damage as Crono, if not more, with her physical attacks, and even when you have all of them with ** speed, she still gets to go first. Equip her with something that increases her damage, or in some cases critical hit rate, and she'll beat just about anything into a fine, red paste, especially when she gets the Bronze Fist. Sure, her magical abilities suck, but with raw physical power like that, who needs it? Basically, with this team, I just crush pretty much everything that comes my way. The items, especially the elixirs and megaelixirs, are going to be just about all you'll need to get by in terms of healing, and on the Black Omen you can even buy elixirs, which I've done to the point of having 89-99 of them on me at all times.