I believe you can use 16" rim if the back spacing is less then stock. But, 15" and 16" tires are going to get harder to get in the next 5 years. 17" rims leave more room for brakes and tires are getting easier to find. I'm a huge fan of 15" rims but its obvious the industry is moving away from the smaller rim sizes.
These days you have plenty of options in tires and rims. Find a 17" rim that's about 8-9" wide and go with 285/70r17, that size is slightly bigger then stock and shouldn't rub, you could maybe try a 295/70r17 for a by bigger too but might rub a bit.
As for tires, Mickey Thompson, Toyo, Goodyear, bfg, nitto, maxxis, all offer quality all terrain and mud terrain tires that perform very well. It may come down to sizing and price.
Check quadratec for rim options and tire options, they have a good variety and can give you an idea on prices and options out there.
Don't cheap out. Good quality parts last longer and save you grief down the road. Especially if you drive it every day.
Hope that helps.