szap,
One thought would be to do a drop camp through an outfitter in a location that has local elk (so you are not worrying about a migration). Will probably give you one of the best opportunities for the money (relatively inexpensive). Remember most states are draw/lottery now, which makes it sometime difficult to plan a hunt for sure. Colorado still has over the counter tags, and possibly Idaho, but I believe every other state is draw (someone can correct me there if they know for sure...I know Wyoming, Utah, Arizona, Nevada, are all draw).

I would say Rifle is definately the way to start. Get a feel for the country and the way elk behave before trying the bow (unless you are going fully guided). The national average to kill an elk is roughly 18-20% every year with a rifle, something like 3-5% I believe with a bow (that's why I always get a kick out of the people that get an elk every year and everyone on the internet shot a 300 point 6x6...but anyway).

Elk hunting is better than it has ever been, but it is still elk hunting. It is tough to explain exactly what that means though until you experience it for yourself.