I would not recommend suitcase type traps especially to a beginner. If you do go this route do not buy any Bailey beaver traps, Hancock type only. Bailey's suck IMO.
I would suggest you either go swimthrough or a large single door. Depending on your location you may find use for both types.
Swimthroughs are best set in the water as a blind or trail set (channels usually). No lure or bait is needed.
Single doors are used with lure or bait out of the water. You need minimum 15x15. Lure is # 1 with bait being usually used as a change up. Best baits IMO are cottonwood, maple, apple in that order.
Brands, I am biased towards the ones I make but Comstocks are a good trap and really any others you might pick up that someone has home made will probably do you for beaver. Just make sure they operate smoothly before you buy if they are used.
Size, I make 11x11 and 11x17. Comstocks are similar in size 12x18. I used to make 10x10 and have seen 12x12s guys make. They all work. It just matters on what the place you are setting looks like. Some of each seems like a good idea to me so you have something to fit the channel. The larger size ones are a bit more versatile though. As I said single doors need to be minimum 15x15 but IMO bigger is better so 18x18 if you see them is better.
About the only place you generally get a chance at used is at a trappers Rendezvous.
I can think of harder animals to start out a trapping career with, but starting on beaver might be a little tough. I'm not trying to discourage you from learning how to trap. But I think you need to take it a little more slowly. Attempting to take several problem beaver from your friends property without any previous experience is more than likely to educate them and make them next to impossible to trap in the future.
I'm not so sure about that. We all had to start out somewhere. First animal I ever caught was a coyote. Not all of us have muskrat to start out on.