A voice of reason....Same thing I tell everyone in your situation. Ruger American 308 with a Leupold VX2 CDS 150-165g TTSX. You will be in the $800-$1k range and it will be a work horse. It will kill everything you need it to and it will be fun to shoot. I own 3 Ruger Americans they shoot great.
You don’t need a monster rifle to kill elk you just need good bullets and good shot placement.
I have an old Browning A-Bolt in .30-06 topped with a Nikon Prostaff scope and it still works fine. Wish it were a Nosler but hey, she go..270 fan here. Have others but always wind up grabbing ol reliable. Not sure what they go for now but it's a Browning A bolt. Leupold glass on it and it's decent. I am in the camp of go good on optics and find a rifle that "fits".
There can be HUGE differences in performance from one ammo to another! When I first got my .308... I sighted it in with the Lead-Free rounds I intended to use. Then... when I went to then just use a cheapie standard lead round to get a lot of practice time in with it... OMG... the shots weren't even hitting the entire target!!! (at 100yds away) Tried for maybe 10 rds total, then was like Bump this, I know my own skills... I gotta see.. so I put back in the other Lead-Free's..BOOM... right on the money. I could not believe there was the potential for there to be THAT DAMN MUCH of a difference!Once you get your rifle and glass. Don't just get out and go hunting . Find the ammo that shoots best from your set up and work with it until you know you can hit what your shooting at with in you skill level. "and be sure of what you are shooting at and what is beyond"