With the stock suspension you can generally go an inch taller without suspension modifications. You will probably need spacers or new wheels with a different offset and backspace because the front tires will rub the tie rod ends (stock fronts are 8" wide and all the aftermarket are 9" wide. As for tires, I am sold on the Kenda Bear Claw HTR. They have handled everything I have tried and have a long tread life. At HMT this spring we saw every type of terrain from mud in the mountains to road use and they did well. I have them on the wife's 500 and my 850.
Mine: 2018 Sportsman 850SP - 26" Bear Claw HTRs on OEM steel wheels(I really don't like the Aluminum ones)
Polaris Hand warmers, Mirrors.
Hers: 2007 Sportsman 500 EFI, Polaris Winch, 26" Bear Claw HTRs on Moose 427x Wheels. QSC Clutch Kit, Hand Warmers
2001 Magnum 325 MOSE 12" rear wheel conversion. 25" Sedona Coyote tires
2001 Magnum 325 Warn winch and Moose 60" plow
2017 Polaris Ranger 1000XP - Roof and front glass
SOLD 2004 Sportsman 600 Twin