Lots of good suggestions here. I would add that most people just getting into the sport quickly decide to move up a bit from there first rifle, so I would consider that in advance, or just buy something rather inexpensive with the realization that you will likely sell it. If you plan on keeping it for a while, I would look at the Remington Sendero, Savage long range hunter, or something in that class.
If you don't want to quickly grow out of what you buy, and want to shoot long range with hunting application, as well as target, give some thought to what you will be hunting, and what range you will be shooting.
Recoil is a consideration for a lot of people, so keep that in mind as well. Smaller bores, lighter bullets, less case capacity, etc. all equal low recoil while the opposite is true of heavy recoil rifles. Also the weight of the rifle enters in as well as whether or not you want a muzzle brake?
It sounds to me that you are looking at a minimum of 6.5 caliber, and for now, a maximum of 30. This will give you MANY good options with good bullet selection.
You should probably stay with a factory rifle for now, at least until you are more experienced.
Here are some popular options in each caliber which have sufficient punch for long range hunting work and will double for target as well. There are of course many other good options.
6.5-284
280 Remington, 7mm SAUM, 7mm RM
300 WM, 300 WSM or SAUM
Don't sacrifice too much on your scope. If you can't see it, you can't hit it! You also want repeatable, consistent calibration. You can get a good scope for around $800.
Here are a few:
I would probably get something in the 6x-24x variable range with turrets.
Vortex Viper
Sightron SIII (my favorite)
Zeiss Conquest
There are plenty more options out there, and everyone has there favorites. Do some research considering your present and future needs. Good luck..............Rich