Prefolds/covers are definitely the right choice if your 2 biggest priorities are saving money and ease of washing. You should be able to get a stash to last til potty training for around $150 total.
I agree with Resi that the teensie tiny sizes are not worth the money. It's cheaper to buy sposies for the first few weeks.
All-in-one's are pricier, but are great for the diaper bag & babysitters because they go on just like a sposie. You can get them for around $10 each (nearly half price) if you buy them as seconds (minor manufacturing flaw that doesn't affect function--slightly crooked stitching, smudge of dirt, etc). Sign up for sale alerts at cottonbabies (see link below) and Swaddlebees outlet has B2G2 free sale a couple times a year. Most of my all-in-ones were purchased from those 2 places. My entire stash cost around $300 and I have enough to last thru potty training. She fit in size medium at 4 weeks old! lemme find the link for swaddlebees outlet and I'll post it in a bit.
If you're interested in the BG one-size that was mentioned above (these work on most babies), you can get them for only $12 each right now at
http://www.cottonbabies.com/index.php?cPath=51