Want a gun of moderate weight with not too much recoil.  Would an 8-8 1/4 # AR in this caliber be a good multi purpose gun (coyote calling, deer, hogs)?  Do you think it's worth the cost of a new (to me) caliber ie. brass, dies, and bullets?

Ask here.

With out being a smartass here is what I think. Get a 6.8 spc and get it in a 6.5 lbs rifle and you would be better off. 16 inch barrel is all you need.

6.5 Grendel is a fantastic cartridge.  I have two and they are amazingly accurate, and very lethal on various game.   It is supersonic out past 1000 yards, it comes in bullet sizes up to 130 grain, with the 123 grains being the most accurate.   Hornady, Black Hills, and Alexander Arms have premium loads.  Wolf has crap loads for it, but they are inexpensive.

6.5 has moderate recoil and is only about 50% more than a 5.56 round.   Some people can easily get sub 1/2 inch groups at 100 yards, and .5 MOA out to 600 yards plus.  

6.8 SPC is good out to 400 yards, but anything over that, the 6.5 is far superior in lethality and accuracy.  Obviously you probably wouldn't be shooting game over 200 yards, but still the Grendel is amazing.  

Palmetto State Armory has the Hornady 123 Grain Amax rounds in stock for $20 for a box of 20.  Excellent price for top quality ammo.   Alexander Armas is about $24 per 20 in bulk, and $30 a box in smaller quantities.