Rocco, Yes tires would be in order and with that, cost. If you are happy with the 13", You can get aluminum wheels in that size at most any auto tire supply. Just make shure the wheel is rated to carry the GVWR of the trailer /4.
IE: 5,000 GVWR / 4 = 1250lb minimum wheel rating.
Another option is look at a few bass boat trailers in your area. THey are typically lightly loaded tandems where a 13" trailer tire would do the job. They are now equipping with up to 15" and 50 Series tires. You are in a weight range where you can get real creative and have many options without overloading your tires.