IMHO get a thai bag. In the long run, it will be more useful than a the shorter bags used for boxing. I have seen (on the internet) someone selling an unfilled thai bag for $100, so look around. If you buy one, the empty/unfilled ones are cheaper. Just fill it yourself with old clothes.
A very good source for heavy bags (and everything else) is http://www.craigslist.org/about/cities.html
find your city's page and look under sporting goods. In the Sacramento area, I see all kinds of heavy bags for sale dirt cheap.
The problem with many of the low end bags is that often the sand bags (which should be in the center of the bag) are too close to the sides - it's like hitting clay. I have made and custom packed or repacked several bags and can give you some ideas.
One of the cheapest bags I have made was from a large duffle bag I was given (they cost about $25 new from army surplus) and stuffed it with rolled up cardboard. If I did it again, I would use old clothes instead of cardboard.
As for the swinging of the bag, many bags have straps on the bottom so you can secure it with some bungies to a cement block. A shoe repair shop can sew on some straps (or repair damaged bags) for almost nothing.
One last lesson from my experiences. Unless you just enjoy the challenge of making your own equipment - save money and time and buy it. It is almost always cheaper than making it yourself.