Ratchet straps -- if you use a lower quality ratchet make sure that with the loose line you tie a knot at the base of the ratchet as it will build up a small amount of slack and then begin to slip and your scooter will start to lean in the trailer behind you over time as you cruise down the highway. Trust me on this one. The other pain in the butt is de-tangling them. It sucks. I probably have 3-4 hours invested over the years in getting the knots out.
Cambuckle straps -- my buddy Ted has a set that is about 3" wide and you give a nice pull on each side and the bike locks in place beautifully. It took us 5 minutes to have the scooter loaded and tied down in the back of his truck, whereas ratchets always took me so much longer. There was no excess in the strap. It was nice and clean and ever so sturdy. Similar to the cambuckle straps pictured above, but wider and shorter straps.
I also purchased Canyon Dancer "Handle Bar Harnesses" and feel that my scoots are so much safer and sturdier in a trailer or a truck because of the Canyon Dancer. This was a great investment. It makes traveling with your scoots easier too.
The last thing you will want is a wheel chock to lock the front tire in place, whether in a truck or a trailer. You have a ton of options. Economy ones look like these from Harbor Freight Tools:
The one above is my preference for when you are in a trailer. Just screw it into the wood base.
These are fold-able and are small. Great for in the back of your truck. You can stash them under the seat when you aren't using them.
You could make something like this out of wood if you prefer.
With a Canyon Dancer, two straps, and wheel chock you will have easy installs of your scoot and super safe travels.