Tire Sizing questions??

[KDRacing]

Im looking to get a 6" rough country lift for my 03 within the next week or so. Im looking around for tires to go with it and im not having too much luck. Im trying to find something that will fit on my stock rims since new rims arent quite in the budget. I haven't found much out there for a 16" at all. just wondering if anyone else is running larger tires on our stocks? and if so what make and size? I was shooting for something around 35" maybe 37"