Which school do you think is the most balanced among the roles? Maybe forgoing Shugenja.

I like the Kaiu Engineer. Artisan/Bushi who can learn Shuji, make and repair items, and even has a little ninjitsu thrown in.

Shiba Guardian, probably? Both a bushi and a courtier school - deliberately, as they are expected to deal with both these responsibilities if the occasion calls for it - and the Way of the Phoenix school ability works in pretty much any circumstance. Shrine keepers get access to rituals, kata, shuji and invocations but their role in society is very restricted.

I think Shiba Guardian is an excellent choice for balance. So is Worldly Ronin. And the Crane clan is blessed with both the Daidoji Iron Warrior and Kakita Duelist. That's 4... If I was going to name a fifth for a top 5 selection I might tap one of the Shosuro Infiltrator, the Kitsuki Investigator, or maybe the Ikoma Bard.

The Ise Zumi and Kakita Shrine Keepers both have a good blend of martial and supernatural power...

I know this may not be particularly helpful, but I honestly don't think there's any one school that could be called "most balanced". If I absolutely had to pick one school, I would go with the Shosuro Infiltrator. That's largely for role-play reasons though, as an infiltrator is supposed to train to pretend to be anything.

I think the Togashi tattooed monk is a very flexible allrounder, while not excelling at anything in particular. If you discount supernatural aspects, the Daidoji is a good all around fighter/courtier hybrid that can work in all 4 forms of conflict.