Sand Filter - How Big?

I have an Intex Ultra Frame 24' pool. 13,000 gals. Less than 60 days and one of the idiots in my pool knocked the skimmer loose, sucked air, and didnt bother to tell me for two days. So my 2500gph pump that came with it seems shot. No filter, no screens, no air, and pump seems to be running at half steam. Barely even moves my robot now, and wont suck the skimmer down in the water like before.

Since I have to buy a new pump anyways, I wanna go with a sand filter. Couple questions...

1. How Big do I NEED?

2. If I wanna overkill it, then how big?

3. I'm under two trees. I have had problem with filters clogging from pollen and cloudy pool for about three weeks. Pollen "caterpillars" are off the trees, and filter problems were subsiding, and pool clearing up. Will a sand filter be better or worse for this problem next year?

I have a pool about the same size as yours. When I replaced my pump a year or so ago, I went from a 1 hp to a 1/2 hp and it has done just fine. My filter is a 200# sand filter.

If you want to overkill something, overkill the filter size. Keep in mind she has a 1/2 HP inground Hayward Superpump which is full rated. She also has a Polaris cleaner for big stuff and just got a Hayward Wanda Whale for the dusty stuff and both work fine with that pump.
Al