Buy new wheels only if you bend a wheel or change the tire size to a size that requires a wider wheel. For example, if your wheels are 14"x5" and you replace the tires with ST215/75R14, you need at least 5.5" wide rims, and preferably 6" wide rims.
But if you find a deal on tires mounted on wheels, there's nothing wrong with buying those. For example, at Southwest Wheel's trailerparts.com, they sell tires mounted on wheels, as well as tires without wheels.
TrailerParts.com Tires & Assemblies - Radial - 14" Radial
Stick with radial tires. Bias plies are the tires of the 1960s.