They say that necessity is the mother to invention; I would say desire is the father. I desire to brew.
I live in a studio apartment. I have about enough space not to go crazy. This does not lend itself to 5 gallon all grain brewing. It doesn't lend itself to traditional equipment. My mash ton, liquid tank, brew kettle, immersion chiller, and many carboys all reside at my mothers house. It's the house I grew up in which once housed many children and now just houses her. She has lots of extra space for my bigger batches, and in contrast I have almost no space to live.
So I desired to brew in my small space. Through internet research, a bit of scavenging, and my own resourcefulness I've been able to do just that. For less than 60 dollars I can brew at my place, brew good tasting beer, and brew all grain batches.
I found a cheap stainless steel pot at my local grocery for 6 dollars, I found a damaged one and talked them down to 4 dollars. It's a 4 gallon pot; perfect for 1 or 2 gallon batches.
I briefly considered getting a 3 gallon cooler and installing a false bottom, this would have worked. Then I learned about an emerging technique that costs very little, takes negligible space, and yields good results. The answer was Brew In A Bag(BIAB). This technique is a lot like a grain sock, except that you increase the size of the sock, and put all of your grain in it. You steep it at the temperature you want to mash at for the time you would mash it. When it is time you just pull the whole thing out like a giant tea bag. It couldn't be simpler. I made the bag from a nylon fabric called voile. The fabric was in the curtain section of my local fabric shop. The instructions said to make a bag big enough to put my whole kettle inside. I double sewed the seams on my sewing machine and put in a draw string. This bag has the added bonus of doubling as a large hop bag for my american lambics. The cost of the bag was around 10 dollars.
This was the most expensive part. In total it cost me 26 dollars build, and I might have over done it a touch. When buying copper tubing it's important to get the tubing that is NSF certified for potable water. This was available at my local Lowes for 12 dollars for a 10 foot coil of 3/8 inch ID tubing. I also got the thicker high-temp spa hosing, and a universal sink adapter, the kind you'd use with a dishwasher. The assembly of the chiller was so simple it's un believable. I started by taking the coil and bending the last foot or so of each end at a stiff angle, between 45 and 90 degrees, in relation to the main coil of tubing. Then I tighteded the coil a touch to fit it into my pot easily. Next I bent the ends out over the rim of my pot and attached the hoses with hose clamps. Finally I attached the sink adapter to the hose. It took more time to go to the store than to build the chiller.
For this purpose I use one gallon glass jugs; I might consider two gallon plastic buckets for heavier beers, or more active yeasts but so far US05 hasn't needed a blow off. These jugs can be obtained from the internet, or anywhere cheap 1 gallon jugs of wine are sold. As an added bonus cheap wine is perfect for soaking oak cubes; cheap grape flavor, no guilt. My Local brew store recycles old glass wine jugs that they get as returns. They sell them for home brewing or wine making. I can get these four jugs for 8 dollars, or 2.50 each. It's convenient to have extras for primary and secondary fermentation.
Depending on the top of the glass jug rubber stoppers of various sizes work. I also use plastic screw caps with a hole manufactured into them; costing just .40 cents each they're a bargain, and they seem to seal everything up nice. I also purchased a 12 inch auto syphon, it is easy to clean, and easy to prime, perfectly sized for this application. My only other purchase was a small funnel for a variety of uses. The Total here was 15 dollars.
Brew Kettler: 4
Wort Chiller: 26
Brew Bag: 10