In the usual 10 characters set up, full list...
Welkin
Zaka
Alicia
Rosie
Largo
Edy or Hannes
Vyse
Nadine
Marina
Cezary or Melville or Jann
You really don't need other scouts than Alicia, since she's overwhelmingly the best scout in the game. Cezary has bonuses against enemy snipers, which can be extremely handy, particularly before you get Marina. For the most part, Lancers aren't as necessary as you would think, as the distances involved makes it much more feasible to simply use Edelweiss' mobility and shoot the radiators of the enemy tanks once I drive behind them, but if frontal attack is necessary (ie, giant boss tanks) it's better to use Lancers due to the halved CP cost of activating them. I always have at least two forward shocktroopers in most missions, as by the end game the flamethrower is a godsent weapon in your arsenal, and even without it they can mop up defended camps with ease (lone camps are easily taken by Alicia single-handedly with her massive AP, grenade and accurate rifle). Nadine is my engineer of choice because of her potentials (Repair Boost) and activating Sibling Ties for Welkin. I'm not sure if it or Power of Love is better overall, but Sibling Ties has a massive accuracy boost which is great for Edelweiss.
The trick to using Zaka's tank is to equip it with either the gatling gun or the flamethrower. Shamrock's mobility isn't that much better than that of the Edelweiss, and the mortar and AT shell on Shamrock kinda suck for damage and can't get enough accuracy boosts. However, the flamethrower is a total killing machine against any group of Imperial footsoldiers, and the more the better. With a long 180 degree arc that entirely ignores popamole and does even more damage than Edelweiss' mortar, often you can just tie up an entire front with Shamrock alone (ie, that one mission where you have to destroy the two mortar tanks at the opposite ends of the map). I haven't tried out the gatling gun, but I guess it's good for sniping infantry, unless it get interception fire too.
EDIT: As for the two certain non-essential characters, Vyse and Marina are no-brainer picks. Vyse is the best shocktrooper (though not by a large margin), as he doesn't have any real negatives (Child of Nature isn't as bad as you might assume) and his combo of Melee Skills, Challenge Lover (which fires all the time at the latter half of the game), Super Damage and Undodgeable Shot is simply fantastic. Marina, as said before, has 100% accuracy at the end-game which alone makes her the best sniper, as well as excellent potentials for a sniper (she gets evasion bonuses when going solo and bonuses when on a vantage point like a tower, for example).