Those Motherease diapers someone mentioned are really great. They are a fitted diaper, meaning that it is a cloth diaper which is fitted like a paper diaper, just without a waterproof cover. This particular diaper is a terry cloth type material....very comfy, and the covers they sell (the waterproof part) are very comfy. Cloth diapering has come a long way since we were babies. They are much more comfy and alot more options now.
I personally like prefolds (which are like those "rags" you buy at the store) but don't buy the flimsy ones in the store. Prefolds are less expensive, plus you can use them for other things later. I also feel like prefolds are the only things I can completely get clean. The synthetic fibers tend to absorb smells more easily. I really like the prefolds from www.greenmountaindiapers.com. The prefolds are on this page. For kids that size I would go with the XL green edge size. I have a chunky 14month old and I am using the next size smaller.
Covers vary, I have tried the swaddlebees abc wrap and the litewrap, but I have heard thirsties and Bummis are really good too. I have like 4 or 5 of these and just alternate to a dry one at the diaper change. If the previous cover didn't get soiled you can just air it out or wipe it off and let it dry, and then just wash them every once in a while. I use a snappi to fasten the prefold and then put a cover on top. I use disposables at night, but you can use cloth at night too, you just need to add extra bulk and make sure you have a really good cover.
I have not tried a service but I am sure that would be more convienent, and maybe better for you since you have a 2 and 3 year old and *hopefully* won't be in diapers too much longer. May be more cost effective in the long run. I know there are also "trial" services on some of the websites that will send you several different kinds of diapers to try in the size you request.
I also sometimes use the Bumgenius that another poster referred too, but I don't know I think they may be too small for your children. They are *just* fitting my boy at 14 months. They advertise that they go to potty training, but I don't see them going that far. The difference with these is that they are called a pocket diaper. You have a waterproof diaper with a thin liner sewn inside, which is left open with a flap in the back, then you stuff the pocket with an insert of some kind. They are easier to deal with for those who don't really want do cloth diaper, or to give to a dad or caretaker cause you don't have to know how to fasten them, etc, but you still have to wash the whole diaper, cover and insert and I never felt like they got as clean...and fastening a prefold or a fitted diaper isn't hard, it just takes a little learning.
Alot of great how to articles here:
http://www.diaperpin.com/howto.asp#prefold