I'll say "what Reid73 said".
The turnbolt action forms the basis of a "general purpose" rifle, for most people, for very very good reason.
You just need to decide caliber, stock type, stock material, barrel profile, barrel length, steel type/finish, bedding type, safety type, recoil pad, trigger type, brand, overall weight. Then decide optics type (probably a scope), ring & base type, and sling.
I might suggest .270 winchester or .280 rem as the best all-around caliber for most people, barrel length of 22", stock type of walnut or fiberglass, bbl contour of light, finish of blued, and one of these brands, roughly in order of preference.
Sako
Steyr
Weatherby Mark V
T/C Icon
Browning A-bolt
CZ (Ceska Zbryovska)
Remington
Tikka
Winchester
Weatherby Vanguard
Savage
Howa
T/C Venture
Stevens
Marlin
But if levergun, pump, or semi-auto grab ya, they can be good all-purpose rifles too.
Do some reading on Colonel Jeff Cooper's "Scout Rifle" concept and look at the Savage 10 FCM Scout rifle and Steyr Scout. This is the rifle type that the late learned Colonel and many others consider to be the perfect all-purpose rifle.
Caliber choice can be a very personal thing for some; for others it's not. Optics are a whole nuther can of worms, and generally speaking you should spend at least as much on the optics as you do on the rifle, and I'd say no less than 1/2 the rifle's cost on a good optic.
PM me if you want to know why I and many love turnbolts the most, and why 2/3rds of my rifles are turnbolts.
-Budget - Open to what is reasonable based on what I find, I don't want the most expensive golf clubs, but don't want the cheapest either. Get what you pay for
Sorry, but there are many many choices/combinations of scope & rifle in each of several budget ranges. You really have to narrow it down by telling us:
1. Willing to by USED on rifle only, scope only, both, or neither?
2. What's the total budget for rifle, scope, & rings? $300-$400, $400-$500, $500-$600, $600-$700, $700-$800, $800-$900, $900-$1,000, $1,000-$1,250, $1,250-$1,500, $1,500-$2,000, or more than $2,000. Pick one (or at least narrow it down to 2 or 3 price ranges). You can get a darn good Savage/Elite 4200 package for example, that will shoot every bit as good as a Sako/Swarovski package, but without looking as good while doing it.
Good glass can be very expensive, so it's an integral part of the scope/rifle combo choice, and total budget for the package. Some people will go with Savage or Howa to free up more $$ for a Zeiss or Swarovski. Some will go for a Sako or Weatherby, but put a $200 scope on it. It's a matter of personal preference, but we HAVE to know the total budget (approx.) to narrow down to any sort of good reasonable recommendation.