Need Advice on Tires (shoe shopping)

I have the 3'' Toytec Ultimate lift installed on my first Gen. Ready to buy some new tires soon. I am currently running 31x10.50 R15 LT.

I would like to go with a 32'' or even 33'' (if possible), but I don't really want to spend money on new rims if I don't have to and keep my stock 15s on. Also, I do not want any rubbing at all with my new tires.

*NOTE: The specs for the lift I installed recommends: 32 x11.50 x 15 or 275/70/16 on 8'' wheels.

I'm looking for a well rounded tire that performs on and offroad, and can handle well in snow, because we sure get a lot of it up here. Although I hit the bush often enough, I don't need a crazy aggressive tire that will be super loud on the road and give me horrible gas mileage. Just looking for a good balance.

So after some research, I found the Open Country A/T II, which seems to fit exactly what I'm looking for in a tire, but it doesn't look like they offer what I want in a 15'' rim size. From what I can tell, I'd have to shell out more cash for some 16'' rims. I'm also not sure if they would rub and/or if spacers would be required.

Can anyone provide some insight or point me in the direction of some alternatives that are comparable to the type of tire I'm seeking?

Thanks in advance.