suggestions for pump and overflow

Pump size will depend on the sump setup and what you're doing for additional flow in the tank, i.e. powerheads, closed-loop system, etc. Also, what kind of tank is it going to be - fish only, FOWLR, reef? That will also make a difference in how much flow you'll need to shoot for. There are several differnet styles of HOB overflow boxes, the cheapest I've found them is on ebay. Most are rated at either 600gph or 1200gph depending on how many drains it has. Which one you choose will be determined by your return pump.

Good prices on those overflows, they are the same type that I use. You can also hook them up to a Tom Aqualifter to automatically prime them.

As far as check valves, with a properly designed sump setup, you shouldn't need one. On the return line, you drill a small hole just below the water line for a siphon break so it doesn't siphon a lot of water back down. Then, you just need to be aware of how much head space is in your sump, so if you do lose power, there's enough room for the little bit of water that flows back down. I have about 250 gallons worth of tanks on a 40gal sump, and when I turn the power off, I get about 3-4 gallons of water draining back because I have my overflows and siphon breaks set up well. On a 55gal sump, you should have plenty of extra space left to catch anything that drains in an outage without requiring a check valve.

You can use them; to me its just one more thing in the line to reduce water flow, and one more piece of equipment to fail if I'm counting on it. You can use them on both lines.