Help determining best approach for processing large raster dataset

I have polygon features, statewide, that I need to collect stats against a raster data.
I thought the best practice would be to loop through smaller selections and process in pieces. (HUC polys).
I have read through lots of blogs, forums, help and I am still confused as to how I should process the raster data.

Mosaic Datasets - Can be used if I have a service set up? I am using a file geodatabase.

Could I use a raster catalog to select the tiles needed for the analysis area (HUC), then mosaic and process?

Should I just pass a single raster dataset and let the zonal tool do the clipping on the fly.

Please help me understand which format can be used.

Maybe I am overthinking this, maybe I can pass all polygons and the entire raster and see what happens?

Thanks
Alicia