I used cloth exclusively -- starting with a diaper service for the first couple of months (literally, it's expensive), and then for the next nearly 3 years with each girl.
Two things about cloth that are *usually* considered a problem: carrying them, and washing them.
There is a perception that somehow having to have the space to bring diapers along means there is no space to take them back. I found used diapers took up exactly the same space the clean ones had, so I was carrying the same amount as if I'd never changed anyone while we were out. Once or twice, because I used the cheap, flat flannel ones, I even 'disposed' of a diaper or two -- usually because of what was in it or where I was at the time. I carried a handful of medium-sized zipper plastic bags (freezer weight) to take home diapers, so the odour wasn't apparent.
Cleaning diapers has turned into some kind of mystical, complex thing. Not only did it turn out to be 'just one more load of laundry', I didn't find it onerous to do even while camping across the country for a month once, with a 2yo.
You need somewhere water-tight to store diapers between use and wash. Many people use diaper buckets but for a variety of reasons, that didn't work for us. We used a large rubbermaid tote, with a snap-on lid. Filling it about 1/4 full of cold water, into which we tossed about 1/2 a cup of an enzyme pre-treat (called Diaper Pure, but there are a bunch) which stops so much ammonia forming, and helps to pre-treat the stains (which I didn't care about, as I knew what was going to happen to the diapers the next time they were used -- stain removal, what a massive waste of energy!)
When it became full (running out of diapers just didn't happen, we had 8 dozen -- one real benefit of using the super cheap ones), it made about 1/2 a load in our extra-capacity washer. We'd pour the whole thing into the washer, rinse it once in cold water, wash it in hot water with detergent (it leaves less residue overall and I could use a lot less for the same clean -- usually 1/8-1/4c of ultra concentrated), and then rinse it in plain hot water (no fabric softener).
We either dried them in the dryer (no dryer sheet) or hung them on the line. Line-dried diapers are a great deal more absorbant than dryer-dried. The other major benefit of the super-cheap, flat flannel diapers is that they dry in a fraction of the time the pre-folded, lined and super-absorbant kind do.
I used the simplest fold I've ever seen: in half one way, in half the other way, then in thirds. When I used them, I'd unfold 1/3, lay the baby onto it so the thin side was under the bum, give the material a 1/2 twist and bring it up to clip at the sides. I used Di-Di clips instead of pins. We used vinyl rather than nylon or plastic covers, just because they lasted longer, and only had about 10 of those.
If the diaper was 'only wet' I would rinse the cover in very hot water in the sink and hang it over the shower bar to dry. If it was dirty, it went into the diaper bucket and was laundered with the diapers.
Oh, the one other thing that paper diaper manufacturers have created is the idea that the purpose of diapers is to keep baby's bottom dry. Nonsense. That's just the distinction between paper diapers and cloth... it's not an important one. Diapers are to keep from having to wash upholstery, bedding, mattresses, shoes and carpeting multiple times a day. There is no reason to let a child hang around in a soiled or wet diaper, but the diaper is to protect the rest of the world, not the child.