Tire Advice?

I have a 2012 sportsman 500. I’m about to put new tires and rims on it.

I wondering what the biggest ( front and back) tires I can put on without add spacers or anything? Without making it tippy?

I also was hoping for some suggestions for the best all terrain tires? In case this helps with advise. I live and ride of great Canadian shield country. So lots of steep rock climbing, also lots of dirt and water holes. There are lots of good mud holes as well. Although mud is a small part of my riding I do enjoy going threw instead of around it.

Lastly I use my bike a lot in the winter for plowing snow and riding to fish hut. I was thinking a 6ply (low as I comfortable going because of punctures) as my understanding is the higher the ply the worse it is in snow?

There are the tires I’ve been considering

STI Outback Tires ( riding buddy just replaced his tire and rims with a set of these installed for just under a 1000) He loves the ride everywhere (little rough on pavement) and just ate up any mud we went threw.

GBC Grim Reaper or GBC Spartacus

Maxxis Bighorn Radial 2.0 ( dosen’t sound like they great in mud)

Kenda Bearclaw K299. If I decide to go cheap. found a few articles say great tire at a great price?

Thanks