Honestly, I'm too lazy to think of a proper team for you, as I'm a lightning main and I'm not knowledgeable about the Fire main's chases and talents, sorry.

Buuuuut, I can tell you about ninjas that are used ALL the time by EVERYONE. Ninja like you Kabuto and Kimmimaro, for example.
Upgrade your Tobi. By god, upgrade him. Until they nerf his ability to dodge mysteries and revive, he's one of the best characters you can get in the game while still being f2p.
Upgrade that Gai. He may not be on your main team as often as you wish, his leech comes in handy in things like SA, and his taijutsu buff is pratically a requirement during the World Boss, if you're f2p.
Upgrade that Hinata and that GNW Neji. There aren't many ninja that can cause acupuncture, so treasure the ones you have. You'll end up using them for FOREVER, especially Hinata, until the GNW version comes out.
For Ranked, you want to use Kankuro. Max him out. His mystery does an absurd amount of damage as well as poisoning the whole team. If you use the GNW version, he stacks on a layer of ignite on top of that. Since the AI on Ranked is dumb af, you'll end up sneaking 1 or 2 of those mysteries, which is a great help.

As secondary characters to keep maxed, but not super important, are Kakashi and Sasuke. They work with * near everybody, so you should at least keep 1 maxed out to use for combos and stuff.
In the same vein, 7 Mist Zabuza. As one of the few ninjas that can cause immobile, keep him on standby. He's dead useful in Ninja Exams and SA. I don't have him, unfortunately, but it seems like every god* guide has him, and I'm forced to try new things to compensate.

Basically, keep ninjas that have unique and useful qualities to them. Useful chases, useful passives, etc.

Speaking of unique and useful, you might as well stop upgrading Asuma, Lee, and Shizune. Asuma isn't really useful ever (unless it's WB Asuma). Lee's only redeeming factor of doing 2 standard attacks as his mystery is already covered by Suigetsu, who has it as his passive. And Shizune isn't as good a healer as Kabuto, nor as good at poisoning as Karin, soooo......