I would suggest tandem axles, unless it's a "micro" trailer. (like a 14' Casita) I drive an 18-wheeler for a living, and have several farm trailers. To me, anything bigger than a ATV/lawn mower trailer, needs two axles.
With any single axle trailer, you may very well experience the "tail wagging the dog." Especially if the weight of the trailer is close to the weight of the tow vehicle. (or even greater) An equalizer, or weight distributing hitch, can help, BUT the buyer's remorse will be terrible if you can't comfortably tow your new trailer. I went with my cousin to pick up his new 24' ultra-light camper. It's a tandem that only weighs about 4500#. (about the same as his F-150 Super Crew) I encouraged him to get a WD hitch at the dealership, but the salesman convinced him that he didn't need one. (and he didn't want to spend the $$$) I thought he was going to cry before we made it 10 miles down the road. He was talking about trading his new F-150 in on a F-250. After a white-knuckle 300 miles home, I insisted that he get the hitch. He's happy with it now and has made several trips, without incident. Point is, don't take someone else's word for it. Especially a salesman who has no skin in the game. It's not his truck or his trailer, once you sign the papers.
The ideal situation would be to have a friend that has a similar rig and will let you drive it.