If you want both elk and deer, .30-06 is probably the best bet. Otherwise I would recommend either .270, or my personal favorite, .308. Both of those would work for elk, but are just a bit light.
As far as rifles go, for hunting I would go with a Ruger Stainless (All Weather) Ultralight. You carry your rifle more than shoot it. There is no need for a lot of meat on the barrel if you are not planning to take more than a few shots at your quarry. Rugers need a trigger job right out of the box, but so does most everything. Also, I am not a fan of the silver and black attack, but it gets the job done. If you like blue steel and wood, they have an Ultralight in that, too. The ring system is damn tough, and comes with the gun. Rings for other rifles are seperate, cost $50 on up for good ones, and their design seems like an afterthought to me.
The wisdom that I like to listen to says that you should spend about the same on the scope that you did on the rifle. I like good optics, since that is my connection with the target (until a bullet gets there). To me that means Leupold VariX 2 or 3. I wouldn't go for any power above 3-9. I consider 2-7 more ideal. If you are hunting elk in timber, you'll appreciate the availability of the low power setting.
Good shooting