Lots of good advice here already.
@fatlander outline of expectations is spot on. I’ll offer my perspective as a relatively new elk hunter with a few years of back and front country hunts under my belt. If this is your first gig I would take the gear you already have if possible so you can figure out what works best before you start spending money on quality gear.
For 2 people we use a 3 person tent (always undersized compared to reported capacity) with a generous rain fly. Most extra gear goes under the rain fly esp electronics. The rest can go in thick 3mil contractor trash bags which are cheap, packable and fairly light. If you have to buy, most any reputable outdoor brand makes a decent tent. Be mindful of weight if backpacking. I have had good experience with mountain hardware, north face, and the REI store brand believe it or not. Outdoor gear lab website has in-depth backpacking gear reviews.
As others have said, choose the week you can hunt the longest. If that isn’t a factor
read this Corey Jacobsen article from last year (or any of the last few years) and try to predict the future. Elk are wild animals and timing the rut while accounting for other factors is challenging. The “best week” one year can be an off week the next year even in the same area. Earlier in September the elk may be less pressured. Mid to late month they will have been pressured, but rut intensity may be increasing and therefore more susceptible to calling. We usually shoot for the second into third week of September. We do account some for our best guess of rut timing, but weigh time in the field as the biggest factor. Each day of hunting a new area does not have the same chance of success but should increase over time as you learn the area and pattern elk movement. Even one more day could be the difference between success and coming home empty handed.
Unsolicited advice from my first Colorado elk hunt several years ago. My biggest take away: fitness is paramount, especially if you do not live at elevation. You will still be out of breath at altitude but you will tolerate it much better if you are in excellent shape. Lots of good threads on this can be found searching Rokslide. Good quality worn in boots, excellent fitness, and being prepared with plenty of water, electrolyte supplements, snacks and enough calories to support your planned activity level will make a big difference in your level of enjoyment and potential for success on the mountain.
