For my money, 3/4" pipe does not exist. For the drain from the overflow I like to go with 1 1/2". A 1" for the return line should be ok if everything is in the cabinet below the tank.
As for a check valve, you have to take into account what is going to happen when the power goes off. Both your drain line and return line are going to provide a path for water to make it's way down to your sump. At some point the water in the main tank will get low enough to allow these lines to start sucking air. That is pretty much the point where your sump will stop filling up. The higher in the water column your return line is, the less water it will suck out when the power is off. If this line has to be too low in the tank, a check valve will help. As mentioned though, there is no free lunch. Check valves come at a cost of head loss which equals reduced flow.
I like to use valves everywhere. A common practice is to place a valve right at the tank, one on a T for water to go to the fuge, and another at the sump. This allows you to balance water flow to the different chambers in your sump as well as provides a shutoff for the whole system without messing with your adjustment valves. For me it seems that you can not have too many valves. While messing with things I have never wished I did not place a valve someplace, but many times wish I had put a valve where I did not.
Consider a union in lines that you may be likely to have to remove at some point for maintenance. Like any pump that is hard plumbed, or an overflow line that would have to be cut to remove a sump.