You can use a variety of different mediums in a hempy bucket, they are quite flexible.
I've seen slightly better results using coco vs perlite. But perlite is easier to maintain, in that you don't have to chase the cal/mag equilibrium.
If you are using coco coir, you will need to use a different medium in the rez area, because the weight & density of the saturated coir is tough on roots. Perlite has been the general choice for some time, but it's been documented that the roots will stop at the coir to perlite transition, this reduces the volume for rooting, but the plants still grow great. I and others have been trying different rez mediums, I've been mixing coco chunk (mulch) with the coir and filling the bucket top to bottom, with really good results, and most likely the winner is Gordon's grow stones in the rez, (it just small rock wool cubes). Which I'll be trying here soon.
Perlite IMO is easier to use, the verm is used to help retain water above the rez level. I don't use it anymore, but I do put a soil cap (top 1 1/2 to 2 inches) which keeps the perlite from floating when watering, keeps the light out of the perlite, and acts like a moisture sponge which helps with the wicking action of the perlite.
Hope this helps.