Flushable liners aren't flushable in the uk, they clog up the sewerage system and end up on beaches like baby wipes and tampons.
Nappy types:
All In One (AIO) consist of a PUL (polyurethane laminate) cotton or minky (short pile fake fur) outer, absorbent tongue usually bamboo or microfibre, and a fleece inner. You stuff the tongue in between the other layers and put on exactly like a sposue, with either Velcro or poppers.
Pocket nappies are like aios but you have separate absorbent bits (thick ones called inserts, thinner ones called boosters) and you can adjust how absorbent you need it to be - some babies pee more than others. Inserts are made of microfibre (absorbs a bit very fast), bamboo (absorbs a lot but a bit slower) or hemp (absorbs loooooooooads but really slowly) and you'd usually need some combination of two of those things.
Fitted nappies are a disposable shaped thing made of absorbent material. You lay a fleece liner inside, then the fitted, then some kind of waterproof layer: rubber pants, PUL wrap (again nappy shaped), fleece or wool trousers/pants.
Flat nappies are either your traditional ferries or prefolds - lots of layers of cotton all stitched together into a rectangle. You can with fold and pin these (nappy nippas are better, no sticking risks!) Or use them to stuff pocket nappies.
I wash at 60 with a prewash and two extra rinse cycles and use half a dose of powder. Liquid and too much powder can clog the fibres making the nappies smell and less absorbent. Line dry when possible especially if you're using PUL as tumbling melts plastic.
Nappies are like jeans - what fits me perfectly will make your arse look huge iyswim. So the best bet is to either buy lots of different brands second hand or do a trial kit from your local library (I'll look for a link in a minute, this post is a hit long!). I would definitely recommend you do not spend hundreds on a single brand's btp kit before you know if that brand fits your baby.
Sorry, that's ever so long
I've tried to condense 3 years of research and practice into a single post. Please ask me questions I'm a bit of a nappy addict!