Or you leave the tank right up on the surface and do a CHIFT PIST system with only one pump and you get a sump.

You will probably want to make sure the autopots are getting filtered water or clogging could be an issue.

To calculate size of sump tank will kinda depend on a few things. Mostly how much grow bed volume you will have.
If you are going to go traditional timer operation with so special valves (like the spider) then you need to figure enough water to flood all your grow beds at once plus some % so your pump can continue to operate. I generally advise you need 50% of the total grow bed volume in order to have enough to flood the grow beds and then I like to add several inches of depth so the pump can operate and I have a little leeway to set up an automatic top up float valve installed above the pump running dry level but below the normal sump low water level.
For a system with about a 2:1 gravel beds to fish tank, the sump should be about the same size as the fish tank.

If you want a much smaller sump tank, but still like the CHIFT PIST idea, you might look at an indexing valve like Rupe has for sale. This isn't quite a standard utilization of the indexing valve though. I have one running on a CHIFT PIST system but it isn't quite a simple set up. It might work using the pump on a timer feeding the fish tank which feeds the valve but I have not yet tried to do it that way so don't know how well it would work that way.