I wanted a good .375 and didn't want to spend more than $1000. I found a used Remington Custom Shop Safari KS rifle with synthetic stock. It's pretty darned nice. Feeding and all mechanics are smooth as silk. The stock is by McMillan. The iron sights are OK, but not great. Mine is very consistent and holds its zero perfectly regardless of humidity or temperature. Some will say it's a piece of junk because it's not control round feed, but this particular gun can be reloaded while upside down, running, shaking, and otherwise in odd positions.
Because you're a lefty, you may want to take a look at these. They come in left-handed action.
It's a 9 pound rifle without a scope or ammo. Recoil is not bad at all. I like the barrel mounted sling swivel ring.