ANGO918,
I actually joined just to answer your question.
My dad and I went to Colorado last year to hunt elk for the first time. We had a great (and successful) trip, but I posted questions similar to yours in other online forums and didn't get much help. I will try my best to fill you in from a beginner's perspective.
We had never been elk hunting before, and selected Colorado for several reasons. Guaranteed draw in certain areas, over the counter tags in certain areas, high population of elk, and (relatively) high success rates.
We did an almost DIY hunt. We contacted an outfitter, and arranged for a drop camp hunt, meaning that they packed us up the mountain on horseback, provided a wall-tent, and packed our meat back down after we harvested. All of the scouting, hunting, and butchering was done on our own.
Colorado has very high elk populations, and high success rates. Keep in mind however, that a high success rate for elk hunting was 20%, meaning that 4 out of 5 guys will walk away empty handed. Two things can tip the odds in your favor: physical fitness and hunting experience. We were up every day before dawn and only returned to camp after dark each night. We covered MILES of ground, and were willing to push hard to make it happen. The outfitter we used to pack in told us that if we hunted every minute of daylight, were willing to put in lots of miles, and were patient hunters, we should have AN OPPORTUNITY to shoot AN ELK. We ended up having a few opportunities, but he wasn't far off the mark. He admitted when he came to pick up the meat that he was surprised we had harvested.
Additionally, we harvested a cow elk. They are more plentiful, and often dumber than mature bulls. I highly recommend a cow tag (or either sex tag) for your first time.
DIY hunting is much cheaper than guided hunting, but your odds diminish. You don't have an expert to help you out, and you have to spend time cutting firewood, tending camp, and preparing food. Another aspect to consider is that during rifle season you will be at elevation (we camped at 9,000 ft) as winter sets in. It might be 60 and sunny, or a storm might roll in and dump 10 inches of snow on you. If you do not have experience with winter backpacking, you can quite literally freeze and die up there.
As for what rifle, there are plenty of suitable options. A reasonably lightweight bolt action is the simplest option. 308, 30-06, 6.5CM, 300 WSSM, 300WM, are all enough gun, depending on how far you want to shoot. We used 30-06, and it performed beautifully. Generally, you need 1500 ft-pounds of energy for elk, so at whatever distance your round drops below that, is a good limit. Additionally, you need to be able to hit an 8 inch target every time no matter what, so that is another limiting factor. Our elk was shot at 200 yards, although we were capable of farther.
We are headed back out next year, so maybe we'll unwittingly pass by each other out there. This time we are doing a completely DIY hunt, packing everything in and out on our backs. It will definitely be an increased challenge, but I think we are ready for it. Even if we don't harvest an elk, it is the hunt that matters, not the kill. Hopefully all this helps, and best of luck out there!