If you are talking large size (not typical East Coast 125-150lb) deer and large black bear, then you want a 30 caliber minimum and preferably a magnum or maybe 7mm WSM
. NC coastal Black bears are going up to 800 lbs with at least 10 over 500 lbs each year.
A 6mm is definitely and the 6.5 is just too iffy for anything less than perfect shot.
both the 6,6.5 and 30 will shoot much better than we can hold them normally. The key is wind drift and KE (kinetic energy) for knockdown on the other end. Highest BC bullets for the 6 will be in the low .5 range, the 6.5 in the low .6 with the 30 cals being in the low to mid .6 range.
IMO the 300 WSM
is just about perfect for what you want. You can go from the 165-200 gr bullets with both quality factory premium loads and reloads. It has flat trajectory, relatively easily handled recoil with a decent stock, high quality factory loads etc. For some reason the 300 WSMs are running double or longer barrel life than comparable other magnums in the LR BR game.
Short action gun, 26" #4 or larger barrel and quality scope it can weigh as little as 7 lbs to in the low teens.
Stiller predator or Lawton action $750
used Rem bottom metal $50
used Rem tuned trigger $75
Wyatts extended mag box $50
custom barrel chambered/installed $500
Stock $200-500 depending on preference (HS Precision, Brown Precision, Manners etc)
Pillar Bedded $150
Misc gunsmithing $200 (no more than if that)
Rings bases $75-200
Used Swarovski/Kahles with TDS reticle $450-850 (add up to $400 more for new)
Bottom line, gun and scope for under $2000 to max $3000 if you want a custom. If factory, then look at the Savage 12 with heavy barrel in the 300 WSM this year and cost will That gives you the typical SC "beanfield" rifle, which is what it sounds lik you are looking for.
Now if you want to reload, look at the 7 WSM, BC is in the mid to high .6s but you will need a custom barrel in a 1-9 twist. However at 500 yards or so, we are only talking a couple inches between the 7 and 300 WSM. My vote is the 300 WSM.