Flats, in general, can be the least expensive option. This is what your grandmother used. It's a single layer of fabric that you fold to fit your little one. When most people talk about "real flats" they're talking about a square piece of 100% Birdseye cotton, usually about 28"x28". Some popular brands are Osocozy, Diaper Rite, Swaddlebees, and GMD. These all generally run somewhere around $2-3 each. Ikea actually carries a burp cloth (Vandring) that is the perfect size and weight for use as a flat, as well. If you're interested in higher end materials for overnight or a heavy wetter (or just because you like nice things), Hemp Babies offers Hemp Flats for $7.50. If you're lucky enough to come by one, the Orange Diaper Co. also carries Bamboo Terry Squares (flats) for $12 each plus shipping.
So what did I choose? Call me cheap, but I went with Walmart flour sack towels. At $1.97 for a set of two, I ended up with a dozen flats and I'll be throwing in a few flannel receiving blankets. I already have some micro fleece liners for naps and nighttime, and a couple sets of snappis. I just ordered some Dritz Locking Head Diaper Pins, and my husband is picking up supplies for a camp washer... I'm weirdly excited.