The reason to go with a bigger diameter pipe from a return pump is to have less loss of flow due to friction, etc, etc. So if you for instance have your sump and return pump in another room than the display tank you could choose a bigger diameter pipe and not lose as much flow as you would with a smaller pipe. If you're worried about flow go bigger, otherwise go with 3/4" all the way. If you're going to use loc line at the outlet in the tank that is 3/4" too. But you can go bigger and then just put a reduction on the pipe to mount the loc line.
The one I've seen Joey build was a Herbie style overflow, with two drain pipes. Google that for a lot more info on how to set that up. But usually when you talk about pipe diameter you talk about the inner diameter. Different materials and qualities have different wall thicknesses so the outside diam can vary. There's flow charts for pipes you can reference. Just remember that what you should look at is flow when it's gravity fed under low pressure. In high pressure the flow is a lot higher naturally and not what you would see in an overflow or even with our normal return pumps.
For 1" pipe that's gravity fed: 960 gph
FOr 1.5" pipe that's gravity fed: 2100 gph
If you're making a Herbie style overflow you should choose a pipe that can handle ALL of your flow by itself (and then some) even if you have two drains. One of those drains is more of a security/back up drain.
Here's a link:
https://www.hy-techroofdrains.com/water-flow-through-a-pipe/