You have to be honest with yourself and your buddies, first and foremost. What is it that you are looking for, how fit and able are you and your buddies, how hard do you want to work? There's just too many variables to be honest. Antelope is the "easiest" hunt. I remember I took my son when he was 7 with me on a hunt up in Wyoming. This was before that bad winter a handful of years ago that cut the tag allotment to nothing. We were hunting up around Pathfinder Reservoir, and at the time, the hardest part was finding an antelope in a spot where it wasnt just pulling off the side of the road and shooting one. I had to work at making it at least feel like a hunt. Not saying all antelope hunting is like that, but its primarily driving around and short walks to glassing points until you find one you want. Not a whole lot of effort involved (compared to a backcountry elk hunt for example), but you can experience some beautiful country and hang out with good friends, maybe get some fishing in or something else while you are out here.
If it were me, I would just jump right into whatever it is you truly want to do. If its an elk hunt, just go for it. If its mule deer, just do it. I will say, one hunt that I always suggest to people just getting into hunting. Look at Montana doe tags in the Missouri Breaks. That is a fun ass hunt, takes some hard work but not quite on the level of a Colorado elk hunt. The tags are inexpensive, and you can start learning some new country you could come back to for elk or a mulie buck. I spent a week in the Breaks with a doe tag my first time up there, and got a doe on the 4th day after watching deer a couple days. I just wanted to take in the new scenery and start to learn the area a bit. Very doable for anyone willing to put a little boot leather to the dirt.