As others have noted, Cloud is the strongest character in almost every way, especially when you start adding in the "sources" (Power, Magic, etc) into his stats.

For me, it breaks down like this:

#1: Cloud. His Limit Breaks are awesome, and he can equally wield a weapon and use magic. As most lead characters tend to be, he's the strongest.

Suggestions: Things like Counter, Long Range and Added Cut are great Materia on Cloud, given the damage he can put out. Also, keeping a fully stocked Enemy Skill (Big Guard, Beta, etc.) on him as well makes him nearly impossible to kill except in the most extreme circumstances.

#2: Barret. Again, great Limit Breaks (especially his final 2 levels), and his automatic Long Range is a great assist. Doesn't have the highest MP but this can be fixed through enough MP Plus Materia. I also make sure he's got a Enemy Skill on him too. Put him with Cloud and you've got 2 really powerful characters.

Suggestions: Putting a strong combo like "Added Effect-(Fire/Bolt/Ice/Poision/Gravity)" on his weapon just enhances his attack even more. I also like sticking a nice Summon (Bahamut, etc.) on him as well.

To be honest, it's really hard for me after these 2 to give you a 3rd. It really depends what you want.

If you want 3 fighters: Cid, Yuffie, Vincent, Red XIII
If you want a magic caster: Tifa, Cath Sith, Aeris

I will also be honest that I haven't went as "in depth" with some of the secondary characters as I have with Cloud and Barret. Cid in particular has one of only 2 TRIPLE Materia Growth weapons in the game along with Cloud, that in itself makes him quite valuable.

As most have pointed out, you can make almost any character into anything you want with the right Materia combinations.

I just happen to have the opinion if you focus on using Cloud and Barret the majority of the game, when you are forced to use others, it isn't nearly the negative impact because you're only replacing 1.

It is more knowing what weapons and Materia to use where, where the good leveling up/Materia building locations are, and at what points you will be changing characters so you are prepared.