My buddy had a streetfighter. It seemed good for the price. He was able to just barely fit a 35 in the back but it took some time to get to fit. 35 fit up front just fine. I would go 32 front and back if it was me.
Sounds like this bike has more or less, the same clearence as my bike. If so, a 35 would be absolute max, a 32 would be a very good middle ground choice (I run 32s on my commuter) and a 28 would likely allow you to fit full coverage fenders, if you feel you need them. Go with 32s, upgrade the brakes if you need extra clearence and then you should be good to go.
i personally ride panaracer tires, so a few recommendations I can give, (all come in both 28 and 32mm)
panaracer RiBMo - if you want a good balance between puncture protection but lightweight and fast (slick)
panaracer T-serv - for a similar tire, but with treading for more confidence through dirt/sand/gravel
panaracer Tourguard Plus - for a heavy duty puncture resistant tire
panaracer GravelKing - for a fast, lightweight, smooth tire at the expense of serious puncture protection (my favourite tire, and what I commute on)
happy riding, cheers mate.