Interesting question. Definitely more thought out than some of the other questions of this type in this category.
After some thinking, here are my choices [Warning: Contains spoilers for some series]
1. Goku (Dragon Ball) - I think the reason is pretty obvious here, but Goku has a strong sense of right and wrong, and is an extremely powerful fighter. Unlike Gohan, though, he has a pure-hearted dedication to his training and continues to keep getting stronger. Although he's a planet buster even in base form, I really wouldn't consider him a "god" or "miracle worker", despite all the Goku vs Superman debates. Even he has a tough time beating poewrful enemies, and his most powerful attacks come from the collective strength of everyone. Goku would probably be the main fighting force for the team, to keep the big bads busy as long as possible while the others work out what to do.
2. Dr. Strange (Marvel) - The universe is a big place, and undoubtedly magic plays a big part of it. That's where Stephen Strange, the Sorcerer Supreme, comes in. Anything magical or having to deal with magic will fall under his domain and expertise.
3. Saber (Fate/stay night) - Getting some females onto the team, Saber is not only highly skilled in swordfighting and experienced in battle, she also has the experience of a knight and wisdom of a king. She has such a high resistance to magic that she's practically immune to it, and her Noble Phantasms of Excalibur and Avalon pack a very hard punch. (Erza Scarlet from Fairy Tail was a close second.)
4. Kurokami Medaka (Medaka Box) - Not sure if she would really count, but if she does, she'd be a force to reckon with. Her Abnormality, "The End", lets her copy and master any skill she could physically and naturally learn. She wouldn't be able to copy things like turning Super Saiyan, for example, but she would be a match for any skills-based enemy she comes across.
5. Lelouch Lamperouge (Code Geass) - Every team needs a strategist (you can't rely just on brute strength), and there's no better strategist than Lelouch. He's shown his ability several times to come up with brilliant, well-crafted plans long before a battle begins, and is able quickly adjust his tactics if things don't quite go as planned. Also, the Geass power of absolute obedience to make anyone do what he says doesn't hurt, either.
6. Kamijou Touma (Toaru Majutsu no Index) - Touma isn't much of a fighter, and he has terrible luck. The key lies in his use of the Imagine Breaker, which can dispel and negate anything and everything rooted in science or magic. Touma would be relegated to more of a defensive/support role, to ensure that the heavy hitters aren't as affected by enemy attacks.
7. Inoue Orihime (Bleach) - Okay, I'm not sure if she actually would count, because she could partly be considered a "miracle worker". Orihime is naive, happy-go-lucky, and has near zero fighting ability whatsoever. Her main forte, however, is her ability to heal any injury (and even death) by "pushing" it away with her shield powers.
If she doesn't count, then Castiel (Supernatural) would probably suffice. Angels in Supernatural have a plethora of powers, including being able to teleport and heal most injuries (and occasionally bringing back the dead, though it's a lot of work), but they're far from being god-like as they can easily be killed (with the right weapon) or banished (with the right spell). Castiel has experience fighting as a soldier as well, though obviously not as well as some others.