I have the equivalent of a 20 gallon megapot (exact same triclad bottom kettle, purchased from a different source). I bought a false bottom from the place where I purchased the kettle. I run a copper dip tube to the center of the kettle beneath the false bottom. I do a direct fired RIMS and, thus, recirculate with a pump throughout the mash. The valve and pump do not get clogged. When I had a cooler, I used a bazooka screen. When I went to the kettle, I figured that the false bottom would be better suited for pumping the mash liquor (versus the gravity fed system I used with the cooler). I don't know if that's the case, but it seems logical to me.
Something to consider if you are coming from a cooler with a braid and go to a false bottom. You will need to add more strike water to account for the height of the false bottom. For me, this was 2.5 gallons more. If you do go with a braid or bazooka screen and will be pumping to recirculate or transfer, you might consider using a grant, gravity drain into the grant, and run the pump off the grant output.