hi crazybutterflylady sorry no one has come back and answered all your questions.
I used flushable liners with DD1 - seemed fine at the time but I've since been converted to fleece (preferably minky ) for DD2 and much prefer them, they seem so much softer than paper. However I didn't really use them to start with as BF poo is so runny and as it comes out of the nappies easily in the machine a liner is a bit of a waste of time. With DD2 I use a few bamboo nappies so it is nice to have fleece next to the skin as it has as stay dry feel. TBH DD1 was nearly always in fleece lined pockets so the stay dry factor wasn't so important. I've been experimenting much more with DD2!
I think you will find with reusables that a lot of it is down to personal preference. You will never find a consensus of opinion and there is no one 'perfect' nappy. A lot of trial and error is usually needed but the positive is that preloved nappies have a really good resale value (although some people turn their nose up at the mere suggestion of second hand cloth!!!)
Anyway I've got distracted from your list 
basic options:
- old fashioned style terry squares with a wrap - can now get nappy nippas to fasten instead of pins. Very cheap, quick to dry but quite bulky and you (and other carers) need to be able to fold correctly.
- prefolds - an aborbant sewn together rectangle that folds into a pad that can be used with a wrap - again very cheap but quite bulky especially on a newborn.
- fitted or shaped nappies (often sized) examples Little Lamb, Lollipop, they are soft and fluffy can be made of cotton, microfibre or bamboo, size 1 is great for a newborn, can be boosted and requires a wrap on top (the waterproof bit)you don't need a wrap per nappy though as unless there is poo on the wrap you can reuse it so a moderately cheap option.
These first 3 options often get called 'two-parters' as there is the absorbant bit and then the wrap making up the nappy.
- Pocket nappies - very easy to use, can be sized but often come in BTP - birth to potty option so although usually priced more than a sized or fitted nappy they don't require a wrap on top and will do from roughly 8lb to potty training. They have poppers on the front to adjust the rise (height) of the nappy so can be a bit bulky on a newborn but you can adjust the amount of inserts you put in so it's not too bulky. Some have popper fastenings at the waist some have velcro - velcro is more adjustable but can catch on things in the wash, poppers are harder for toddlers to undo themselves but some people find poppers more fiddly (dare I say it Dads and childcarers - aware that is a sweeping generalisation but I read it so often it must be sort of true!)
Most pocket nappies seem to come with microfibre inserts but can be used with bamboo or hemp if you need more absorbancy. Popular pocket nappies are Bumgenius, Rumparooz, 'ebay cheapies',
Blueberry, Wonderoos, Charlie Banana, Issy Bear - all Birth to potty (although blueberry and Charlie banana also do sized)
- All in one - very similar to pocket nappy but with the insert usually sewn in so it is all in one piece, this usually takes longer to dry. Some manufacturers have addressed this by making 'snap in one' or 'all in two' products which are a kind of hybrid. They may popper apart for washing/drying but once put back together they go on all in one piece. They are very attractive for children that go to nursery as the parent can pop them all together and they basically go on like a disposable so are pretty foolproof. As well as the hybrids I have mentioned some AIO have a pocket so additional boosting can be added.
Popular brands are
Itti Bitti D'lish (sized) , Totsbots Easyfit v2 (BTP),
Close Parent Pop In (BTP) and Real Easy (sized).
Boosters and inserts are really the same thing - an insert usually comes as part of the nappy and you may choose to 'boost' withe something additional.
I don't find reusables more a hassle when out and about. If in a toilet you can get rid of the poo down there and just take the soiled nappy home. If you are at the park or some changing rooms don't actually have a toilet you are then obliged to carry poo around in the nappy til you get home but as long as you have a decent bag I find there is no smell. My favourites are
Monkey Foot Bags - some people carry big bags around but I personally just have the small size - 1 for resuable wipes and one for a soiled nappy. I can just roll up the nappy put it in the zipped bag and deal with it when I get home. The XL bag can be used instead of a nappy bucket at home.
Some real nappies will leak just as some disposables will leak as well. I find I get less leaks with cloth nappies but you do have to change them more regularly
however they are generally very good at containg poo (as long as they haven't already reached saturation point with wee).
Night time options - generally pockets can't be stuffed enough to last all night (although there are always exceptions
) so two parters are more popular at night. You can use a PUL wrap or fleece pants or woolen wrap on top.
Bamboo is good for night time use. I like a Totbots bamboozle stretch with a Motherease rikki wrap on top.
Oh and one more 'type' are wraps designed for pad style inserts kind of like prefolds.
Bumgenius do Flips which are birth to potty wraps and they sell stay dry inserts - which are microfibre, they also do organic cotton inserst - which fold up a bit like a prefold, last longer than the stay dry but need a liner on top and then finally disposable inserts for holidays etc. Now available in velcro or popper fastening but just plain colours. Flips seem to be hugely popular right now.
Weehuggers do 2 sizes of wrap and they do their own bamboo insert (again it needs a liner on top) they have some plain colours and funky prints (both popper and velcro)
there are other sorts - Gnappies, Smartipants etc but I don't have first hand experience of them but from what I understand they are a wrap and pad insert.
I've waffled on now, shout if you are confused, I have tried not to use too many acronyms!