I must have tried at least 100 over 10 years and 4 in nappies. Here are the types:
Fitted: an absorbent nappy made from cotton, bamboo or manmade materials. They need a separate waterproof cover, called a wrap, so take slightly longer to put on, but they are less likely to leak and usually cheaper.
All in one: absorbent nappy and waterproof cover in one. Usually sewn in. Easy to put on, but can take longer to dry depending on type. Usually more expensive. Often need absorbency boosters. Harder to dry as most waterproof covered shouldn't really be tumbled.
AI2 All in 2: an all in one but the absorbent insert can be unattached, for drying, and to change absorbency or fabric. Often have choices of inserts. Usually expensive but you buy inserts separately, so it can be more economical if you reuse the cover and just change the insert if nappy is only wet.
Pocket nappy: basically a waterproof nappy cover with a pocket to put the absorbent insert in. Usually microfibre inserts. Quite cheap, usually has a built in fleece liner.
Terry nappy: an old fashioned square, but used with a nappy wrap instead of old fashioned plastic pants. Do up with a Nappi Nippa instead of pins. Easiest to wash and dry, cheapest by far, folds are very easy and there are tonnes of choice to suit each baby.
You can get rainbow colour packs.
Prefold: a rectangle of cotton, you can just pad find it into a waterproof cover that has a gusset. Very very cheap, easy to use, can be a bit bulky, and can leak if cover isn't very well fitted to legs.
Liners: liners are optional. You can use disposable to help poo disposal, but these are useless for pre-weaning poo. They aren't very popular. You can use fleece liners, which keep babies skin dry. You have to shake poo off them into the toilet. Breastfed baby pre weaning poo can go straight in the washing machine.
Bumgenius elemental all in ones are my absolute favourite. They are very absorbent, have never leaked, slimmest out the lot, lovely bright colours and prints, and they can be tumble dried. Bumgenius also do Freetimes which are the microfibre version. Ever so slightly bulkier, less absorbent, but really comfy and come out of the wash almost dry. Great if you don't have a tumble dryer.
I also really like Grovia hybrids (AI2) you just snap in the insert to make it an all in one. Great prints, slim, and easy to use. Also expensive.
Personally I despise pockets, they are just a huge chore to stuff. Much more of a nightmare than Terry squares.
Other brands to look at are Close pop in, Totsbots, Bambino Mio, Milovia, Little Lambs, Motherease.