Utah has both tags available on a draw system and over-the-counter tags for elk. If you want to hunt trophy bull units or a cow you must draw. But if you want to hunt the general units you can with an over-the-counter tag but I wouldn't recommend an over-the-counter to someone who isn't very fimiliar with those areas.

I'd say start putting in for draws all over AFTER you have done some research on each states website. Look for things like hunt success rates, odds at drawing a tag in a particualar area, and what each area is managed for. A drop camp is a great idea for a first timer not wanting a full-blown guided hunt. If you really want to do it all on your own and you just want the experience I wouldn't plan on going after a trophy bull. You had an offer to tag along, that would be a great way to start. If you don't do that then get either a cow tag or an either sex tag and shoot the first legal animal you see. Good luck!