Sylvia, IMO the stick-on products are a better option in most situations because they don't marr the wall.
Another option you have is contacting Jayco for a schematic of the wall you want to hang it on and you might have a wood brace (stud?) in the area you want to anchor your basket or shelf. Then you can use any fastener you like.
I hung a 3 hook coat rack on the outside of a bathroom wall using wood screws because there was a horizontal wood brace in the wall. Even though you can locate them with a stud finder, I would check it with Jayco's schematic so it isn't "something else".
It really depends on a few things. Are you securing to the outside wall or an interior wall, and how much weight it needs to hold. My personal favorite screw for the TT is the Kreg brand screws. They are self drilling and are extremely similar to what Jayco uses. I do use a lot of Command Hooks too.