Colorado is full. So might try elsewhere, but if you're hellbent on climbing the Rockies, here's a few things. CO does not have over the counter cow tags, you have to put in for a draw to get one. Most are "B" tags, which means you can also have a bull tag. Way too complicated to explain here.
A 270 is fine, but go with a partition or copper solid. In an ideal situation a 243 is more than sufficient; however, I've hunted long enough to know the ideal situation almost never happens.
I tell friends and buddies coming with me for the first time to think of the first year as a practice run. Just enjoy it and keep expectations low. Lot of first time elk hunters don't even see elk their first year. If you are coming for the scenery, late bow season is about as idyllic as it gets in CO. Aspens are yellow, weather is 70 during the day, 30's at night. The Flat Tops are a gorgeous area to hunt if you want the scenery; animals are there too, but takes some serious skill to get on them.
You're going to pay $3000+ your first your on DIY hunt. The gear is $$$$. Tent, winter rated sleeping bags, heaters, stoves, and high quality clothes/boots. Your tag alone in CO is about $760 now.
You might want to check out a drop camp where an outfitter "drops" you off at a pre-setup tent. You bring your own food, clothes, sleeping bag and the outfitter covers most of the rest. It's not guided but they usually park you in a good area. What you save on gear costs, you'll be paying the outfitter to rent his gear for a week.
Number one piece of advice, get your a$$ in shape. At a bare minimum, if you can't walk 5 miles with 30lbs on your back at sea level, 9000' elevation on the side of a mountain is not a playground you want to be on.
