From experienced parents, what are the pros and cons of cloth and disposable diapers? I’m looking to keep my child as comfortable as possible, doing a minimal amount of harm to the environment, and save myself money and stress.

We will be staying in our tiny one-bedroom apartment for the first 3 months with laundry available about 100 feet away across the courtyard. After that, there’s no guarantee that the place we move to will have laundry in our home (we’re going into the Army–well, my husband is).

I’ve used both, cloth are better.
I have 20 diapers, they lasted about 2 days with a newborn and last about 3 with my 1.5 year old.

Pros:
-Cheaper in the long-run. To have your own stash takes a bit of up-front cash, a couple hundred for a good stash and accessories, but you can trim this down by buying used or in bulk.
Using cloth diapers is not cheaper if you use a diaper service. Diaper services tend to be very expensive and not many cities have them. Buying your own is the best way to use cloth.
-Nice soft fabrics.
-No excess in chemicals.
-Less rashes. The only rash my daughter has ever had was a yeast rash from thrush and reaction rash to a different detergent.
-Less stink. Disposables reek, and the smell lingers. Tossing cloths in a nice lidded can keeps smells in. You’d never know I have diapers in my house.
-Less mess.
-Less leaks. I’ve never had a leak in a cloth diaper, I’ve been using them for nearly 18 months.
-Environmentally friendly. Kind of. It depends on local water recycling policies, what sort of detergent you use, what water temperatures you wash in, if you line dry or tumble. So, it could be a really green choice for you, or it could not really matter. Either way, it keeps a couple thousand disposables out of landfills and that counts for something.
-Modern pocket and AIO diapers are grandma/daddy/babysitter friendly. Most day cares won’t refuse to use them. Why would they? They’re the same as a toss away, you just toss it in a bag to send home instead of the trash.
-It’s easier to potty-teach toddlers in cloth diapers. They can feel the wetness on their skin and this makes them uncomfortable, they’ll learn the potty much more willingly and quickly.
-They really are very cute.
-You can get one-size diapers that will fit from newborn to toddlerhood. So, one stash can fit multiple kids and last them the entire time they’re in diapers.

Cons:
-The up-front cost can be significant if buying a stash of brand-name one-size pocket diapers.
-You do need to change the baby more often, since they can feel the wetness you can’t put off a diaper change like so many do. I personally don’t see this as a con, but many would so I mention it.
-You need to be aware of your laundry routine. Too much detergent can ruin your diapers, so can not enough so it takes a bit to get used to for some people.
-You can’t use any old rash cream if rashes do happen, most will ruin absorbency of cloth diapers, so you need to be aware of that as well.
-The one-size diapers can be bulky and distort the look of clothing. It’s nice to have some fitteds or prefolds and covers on hand for special occasions when baby should look perfect, like photos.

That’s pretty much it.
To cloth diaper on the cheap, look at the Flip and Econobum kits here: http://www.cottonbabies.com/

Good information here: http://www.pinstripesandpolkadots.com/basics.htm

I get my diapers here: http://www.jilliansdrawers.com/
The customer service is wonderful and their prices are reasonable. They often have gently used and discontinued items for very low prices. They also have a "try before you buy" package. They let you try cloth diapers for 21 days. If you like them, you keep them and send them the difference. If they’re not for you then just return them and they’ll refund you $100 of your $110 deposit. A very good kit if you’re on the fence.

As a sidenote, my husband was against the idea of cloth diapers. Not because of cost or anything but because he thought it would be a huge hassle.
He’s _very_ happy we got them. He has no trouble using them at all and he also suggests them to friends when they ask.

Also, there’s a lot of information around suggesting long involved laundry routines, I don’t actually suggest you ignore them, but. I will tell you that I’ve put my diapers through one cold wash cycle with a normal cold rinse cycle in regular detergent with no ill effect on my diapers.

I’ll never use another disposable diaper if I don’t need to.

ETA: Also, it doesn’t have to be an either or thing. You can use both and use whichever is convenient for you at the time (ex: cloth during days, disposable overnight or when out). I have a personal preference for all cloth all the time, that doesn’t mean you have to follow suit.