For pump action shotguns, the guys have named the common go-to ones. Remington went out of business, and as far as I know nobody has picked up the shotguns stuff so they aren't making 870's right now. There's a crap ton of them in the used market through. They're a very reliable gun. The Mossberg 590 series is Mossberg's answer to the Reminton 870. I've had really good reports on the Maverik 88s as well. There's tons of aftermarket options for the 870s and the 590s. If you want to get into higher end stuff, look at brands like Benelli. Not as many aftermarket add ons for those, but they make damned nice guns.

Bolt action....oh boy. That's a loaded question. There are a LOT of good options out there. Don't worry about staying away from "plastic" guns. The polymer stock world is upon us, and there's nothing wrong with most of them. If you want to get into the nicer hunting rifles, look at stuff like Tikka and Browning. That said, there aren't a lot of "crappy" rifles out there. Again, don't worry about "plastic" stocks. I've got plenty of wood and plenty of plastic. They both hold up fine, and the critter you're shooting at doesn't give a dam what it's made of.