Your inserts are fine against skin
I would look at buying hybrid outers/shells if you want to reuse your inserts (and I would), not pockets. gNappies/Diapers are a type of hybrid but they're SO fussy and I didn't find them all that reliable. I much prefer Flips (which are made by the same people as bumGenius and have much the same fit), but there are lots of good options now e.g. Grovia hybrids, Blueberry Capri, Planet Wise Covers. Generally a hybrid consists of a waterproof outer with flaps in the front and/or back to hold the insert in place - none of the silly fussing around with pouches like you get with the gs! A lot of 'normal' covers have flaps to tuck inserts under but you actually don't need them so you can use pretty much any wrap/cover that isn't baggy around the bum e.g. you could use Thirsties Duo Covers, Blueberry Coveralls, Rumparooz etc and just lay the insert in it.
You could buy pockets, but if you already have the inserts you'll be buying full nappies as pretty much all pockets come with inserts included. Why pay extra? Also, you can't use a pocket outer for a second time - some say you can lay the insert on top and just change that but in reality, as soon as the back of the insert gets damp you need to change the whole nappy as the pocket nappy's lining will get wet too. Unless it's wipe clean (which pockets aren't), it will not be very nice.
The difference between a pocket and an AIO is mostly about the laundry. Pockets come apart for the wash so you can be certain everything is getting thoroughly cleaned (although I think AIOs in modern washing machines are absolutely fine) and then as everything isn't stuck together they usually dry a lot quicker than AIOs. They're a bit more customisable too, as you can add whatever inserts you want to the pocket. If you want to boost an AIO, you normally just have to lay a booster on top of the inside. For actually using them on baby, they're more or less the same - both a one-part system.
Don't buy lots of anything, I'd just get one of each type you like the look of and try for a week then buy more if you get on with them. Also don't feel you need to stick to just one brand!