On a 120, that's allot of tank for 500 GPH. I was running my 120 with dual overflows at 1000 GPH, but with my headloss, I was really running at 600 GPH, which is a 5x turnover rate, perfect for flow for sump and skimmer
My 180 is being ran the same way now, just a bigger pump
Go with a Ehiem 1262 , which is 900 GPH, and with head loss you'll be around 500GPH
Or I just ordered a Reef Octopus DC5500 which is 1,450 GPH for my 180
In your case a DC3500 would be perfect, and you can adjust the flow if needed
No on the check valves, they are prone , or just another point of failure