AIOs take a long time to dry, regardless of brand. In the dryer, it can take 2 full dryer cycles to get them dry. You can dry them on the clothesline, but then they are stiff and you'd probably want to run them in the dryer for a little bit to soften them up. I don't know how long it takes to dry on the line, though.
If you're averse to pocket diapers, then I would suggest instead of AIOs, you do fitted diapers with covers. You can use Prorap "second" covers (see below) and use them with most/all fitteds, and there are one-size fitteds you can buy. A friend let me borrow her MotherEase one-size fitteds; they work really well for us from age 6 months & up (she lent them to us at 6 months, so I can't speak for when the baby is newborn). The ME fitteds have a snap-in layer for more absorbency, and they stay snapped in the dryer, but because of the design, they dry pretty fast. Kissaluvs has a fitted (but not a one-size I don't think) with a similar partly unattached extra layer, and this style does well drying fast in the dryer. I do not like the ME covers, though, as they tend to hold the smell.
If you really are trying to be cost conscious, I highly recommend prefolds and covers. They are the least expensive way to go--both in terms of initial cost and in terms of energy usage for laundry--, and take the least amount of time to wash & dry. If you don't like the thought of using diaper pins, they make these rubberband-like attachments called "Snappi" or "Snappi's" that you can use instead that doesn't have the "stab" hazard that pins do (that being said, in the thousands of diaper changes for our son, I've never once stabbed him, though I have stabbed myself once or twice accidentally). You can buy really good quality prefolds and diaper covers "seconds" from Prorap Services, phone ###-###-#### (in Washington State) or (800) 397-8594. I don't remember the lady there, but she is super nice, super accommodating, and can help you find the right size diapers & covers. The "seconds" covers, which work just fine but sometimes have slight cosmetic issues (i.e., wrong thread color) are currently $5.25 per cover, which beats pretty much any other cover out there except maybe the Gerber rubber pants (and I'm not pulling a nasty poopy diaper over the bottom & legs so no Gerber pants for me!). Prorap sells prefolds (they are really good, "diaper-service" quality diapers) for a good price.
The other option you could try is one of the starter packages, which offers some prefolds, some fitteds, a couple or more of different covers, and usually a pocket or AIO or two or three (depends on the package). This would be an economical way to try a variety of styles without breaking the bank.
I also suggest checking out myuseddiapers.com and diaperswappers.com. They are ebay-like sites where you can bid on and buy used diapers. It's a less expensive way to try out a variety, or pick up more of the kind you've come to like without paying full retail. Also, if there is a diaper service near you, call them and ask if they sell their used diapers. A lot of times, if they can't get the stains out, even though it's clean and safe to use, they won't put it back into the inventory.
Also, don't be shy about checking out the children's consignment shops around you. Call & ask them if they have cloth diapers. If you have any "natural baby stores" in your area (selling wood toys, fair trade baby stuff, pregnancy tea, etc.), they may carry diapers. The one in our area offers a diaper swap 2x per year, where people can sell their used diapers.
Some of the brands have websites where you can sign up for notifications of sales, seconds, etc. Kissaluvs has this, and some of the others do too.
A good overall website is Green Mountain Diaper. Lots of good info and good prices on new: http://www.greenmountaindiapers.com/.
One thing that clinched it for us to jump in was the fact that we use flushable diaper liners. So no handling/scraping/hosing poop into the toilet--liner and poop just go in with minimal (like no) handling. That was what made the difference for DH.
DH found prefolds "confusing" so I did fitteds/AIOs/pockets (prestuffed) for him, and for me, I do prefolds.