Hnnnng. Don't do this to me if there's actually no game related Banjo thing at E3, I can't take the disappointment!
Banjo 1 remake would be my biggest wish. One of my favorite games ever (if not THE favorite) so having a Crash/Spyro/Ratchet+Clank style modern remake of it would be INCREDIBLE.
Runner up would be Banjo in Smash. Perfect fit, and they'd probably be a really fun character. Maybe release Kazooie and Tooie XBLA versions on the Switch too along with it.
Third place would be Banjo Threeie. Why isn't this first place for me? I honestly just don't trust anyone to make a NEW Banjo game that's anywhere as good as the first one. Rare didn't manage it with Tooie (levels way too large, overworld not as fun, way too many new moves complicated things too much), Ex-Rare couldn't do it with Yooka Laylee (most levels were a bit too large again, overworld wasn't great).
I'd take that over an attempt at a true platformer Banjo 3.
Nuts and Bolts was absolutely fantastic, and in a post Minecraft world, I bet Microsoft could do some incredible things expanding on the vehicle creation aspect of that game in a sequel.
I'd have much more faith that a Nuts and Bolts 2 would be fantastic than a platformer Banjo 3 could live up to my expectations.