...Well framed search ??'s so far JE...
I suspect there's gonna be lots of good info responces...but based on the limited reference of you having handled a couple of rifles...lemme ask a couple ??'s before the peanut gallery chimes in...
What brand and caliber rifle have you had ANY experience with and was that particular rig satisfactory for your needs? or just gooder enough to whet your appetite for what else is out there?
Final Figure Budgets available? IE: Scope/Rings & Rifle total $'s available?? Do you own or use more than One Shotgun?
Gonna have any other users for this rig ...ie...wife/son/father/ brother/cousin etc
Do you have family/friends who's opinions you'll have to satisfy or be subject to their approval and influence...and WHAT rifles and calibers do they shoot?
At this point it all depends on your Total Dollar Budget for brands ...buty I'd suggest a bolt action of some sort...in the bigger than a 22 Centerfire cal & smaller than a magnum caliber from say 243 to 30'06 and probably one of the core 4-5 most popular calibers that provide the cheapest and most available factory ammo...ie 243/270/308/30'06 or mebbe a 2nd group of 25'06, a 6.5 something (260/6.5 CreedMore) & 7-08.
I like hunting bullets that weigh more than 120 gr's with the 120/130 gr'ers through 165gr's being the most common weights I've used, and are capable of 28/2900 fps or better out to my comfortable hunting ranges of 3-400 yards. 90% of ALL the game I've shot at is usually uder 150/200 yards....but then I'm Old School trained and ingrained with my 1st WTail kill in 1967 at 23, at a bit under 200 yards.
This may sound funny since I've never owned but one or two...but IMO the best Do All for your needs is probably a 308, as has a lifetime of use in a 270, that has never failed me, given the parameters I've referenced. ...but neither would have a 308 or a 30'06 either....but they are not the sexiest most exciting Joe Cool at the Campfire choices either.... just plain jane reliable with the lowest cost and most available ammo. Have fun!