you may also want to search the used gun racks .
THIS.
Not Necessarily THIS:
for a good 30/30 more than enough power to knock down a deer or bear not much recoil and lots of them around for well inside your budget get a marlin and you can scope it real easy also
Nearly ANY Centerfire caliber with one of the controlled expansion bullets (Interbond, TSX, Partiton, etc.) will be sufficent for 100 yards to kill white tailed deer or black bear, given proper shot placement. Most of those calibers will suffice with a neaderthal cup and core bullet, provided the bullet has enough mass and velocity to penetrate though vital organs......
As for "Quality scopes" ... my deer rig features a scope that can bought on ebay for 25 bucks ..... yet has been used to whack more deer than most Americans have seen .....
The key is placement .... and that comes with pracitice to the point of familiarity ....
IMO, you would be far better served buying a $300 pawnshop used rifle (with scope) in any caliber =/> than .243WIN.... AND a handloading setup and handloading than spending $500+ on a new rig and glass ....
My brother bought a Remmy 721 in .270WIN at Green Mountain Guns in Denver ...... with 3x9 Waver scope, Lyman 310 handloading set-up, several hundred rounds worth of components .... and load data ... for $350 .... He killed two deer with it the year he bought it .....
If you can shoot with open sights, then a Commie Aught Six can be had for less than $200 and will kill any animal that walks the earth ..... provided you do your part..... the '36 Tula Hex refurb I bought last week for $213 tax included printed a 3" group from a sitting position today at 100 yards with PPU factory ammo .....
My Eldest daughter killed two deer, on consecutive days, with her Marlin 30A in 30/30WIN last November.... in open county ..... I saw essentially the same gun (a Marlin 336), scoped, today for $450, at Guns Unlimited in Omaha....
My ultimate "kid's deer gun" is a Ruger Frontier in 7-08 ..... stoked with 139gr Hornady soft points downloaded to 2400 f/sec. My 10 y.o. son pops milk jugs full of water with that out to 200 yards with almost boring regularity ..... once I get a can on it, it'll be Perfect.
Note that not one of the guns mentioned in this post can be bought new, and only one will set you back more than $500 .....