The cheapest way to make the trailer is to find your own second-hand wheels off an old bike, but you can get new wheels with the kitset or from a local bike shop. Slick tyres travel much better on the road than knobblies if you have a choice.
For the small trailer 16” wheels are perfect but you can use 12” or 20” if you wish. The bearing cones are likely to need offset if you use a 2nd hand front wheel as there is not normally enough thread on one side to attach it securely. You will need a hub spanner to do this and can put new grease in the bearings while you’re there. A bike shop could help you if you are stuck.
For the medium and large trailer 24” wheels are the perfect size. 20” wheels are good stability wise but sit a bit lower to the ground and are theoretically less efficient than larger wheels. Avoid 26” wheels for these size trailers as they will not fit in the medium trailer and are too unstable for trailers < 500mm wide load space. Most bins will require wood screwed to the sides to raise them >100mm off the ground no matter what size wheels you use.
For the extra large and ginormous trailers, 20” to 26” sizes are all acceptable.
Avoid larger diameter road bike wheels on any trailer (27” or 700mm) as they wobble too much.