If you have no budget to where you can't afford new tires, then you shouldn't be shopping rims (new or used).
If you have some budget, new tires should take priority over bling rims.
If you have budget for new rims, putting used tires on them is like flushing money down the toilet. Blow a tire, spoil a rim and then you have 3 rims... bad all around.
If you're on a budget, 265/75R16 tires are not exactly stock but fit real well and the diameter is about as close as you're going to get to stock. They're common tires and can be sourced on a budget. I have 265/75R16 on my wife's truck and they fit/ride very nice.
Remember, whatever size you do go with, you will need a matching full sized spare. Be sure to put that in your calculations.
With Grench on this. Most tires are not available in 275/70 - 16 stock size but almost all are in 275/75-16 which is very common. If I were on a budget, I'd do the 265s in a hearbeat compared to what you're thinking about.
Another option I have seen, and contemplated, is craigslist for new take offs from a 4runner or Sequoia. I used to see sets for @ $300~$400 with good rubber remaining on them. Folks buy that new truck, and them immediately go for broke on new 20's, then dump the OE wheels.