Someone asked me about starting beekeeping the other day. I was excited to tell them "how I would do it if I were starting again". First off - I'm no expert. Although I've been interested and read about it for 30 years (even helped splice a hive about 30 years ago), I just started beekeeping myself 4 years ago. Even so, it's probably a bit premature to endorse a method I haven't tried yet, but if I were going to get started in beekeeping right now I would use the Kenyan Top Bar hives (great site, btw). I base this on an article I read in Bee Culture a few months back. You can build them yourself. The design promotes health by allowing the bees to make smaller cells which seems to inhibit mite populations somewhat. Also, the act of harvesting removes comb so that you do not have old tracked up comb that can result in sickness.
Because you don't have reusable frames and foundation, you don't need an expensive extractor. Just two common plastic 5 gallon buckets are used (Home Depot has them for less than $3!). There is no expensive equipment to buy - just a veil, gloves, smoker, hive tool and a 4x8 sheet of plywood! From this sheet of plywood you can make 3 hives and have enough material left over to make 2 nucs.
If you're looking to save even more money - build these hives and nucs and give your phone number to the fire department to call for swarm removal = Free Bees! Be sure to purchase the above equipment before doing that. In fact, if you're going to go after feral bee swarms, you'd better invest in the entire bee suit! [Disclaimer: If you live in the southwest (or even if you don't), you might want to just BUY some nice Italian bees from a reputable dealer to start off.]
This book is suppose to cover top bar hives pretty well. It's on my list to buy. Here's a neat video I found on building a top bar hive.