However, I don't want to spend a ton of money and I really only want to do it if I can produce it without increasing the amount of money I spend on beer.
Quit now, while you're still ahead.
I really have two reasons that I want to do this. 1.) Cheap beer, 2.) Education.
You can scratch #1, and put "The best beer you will ever have" in it's place.
Seriously, start-up costs for home brewing are in the neighborhood of $200. You need at least one large bucket or glass container for fermenting, but 2 are suggested. You need a siphon, thermometer, hydrometer, bottles, bottle capper, bottle filler, and a big enough pot to hold at least 3 gallons of liquid. Even after you get all of that, each batch of beer is going to cost a minimum of $30 which makes 5 gallons (about 2 cases) of beer. That is for the pre-assembled kits, which don't make the best beer. If you buy the extracts, grains, yeast, and hops separately, you are looking at more like $50. If you use all-grain recipes, you don't have to buy the extracts which will save you some money, but you have to either buy or assemble a lauter tun. Not to mention the fact that all-grain beer takes a hell of a lot longer to make.
BUT...ignoring the financial aspect of beer making, it is a very fun thing to do, especially for us science dork types. Plus, the beer that you get after all your investment and hard work is some of the best you will ever drink.