I'm wondering what equipment I should get to make it as cheap as possible because I'm not raising on a mass scale and also any tips(like is there a cheaper solution to a kill cone or is there anything I should know about defeatherering birds by hand etc.)
To me, as cheap as possible means using what you already have and get rid of the idea that there is only one way to do things. I don't know what you have. I do not use a killing cone or a rope. I use a hatchet and stump, but I already had the hatchet and stump. The stump was actually a section of tree trunk from a tree that fell down. No cost to me except time to cut it into a useable pie. Some people use an ax or a meat cleaver instead of a hatchet.
Others may use the broomstick method using something they have on hand. Could be a rake, axe handle, maybe even a tree limb. It doesn't have to be a broom and you don't have to buy anything special. Some may use pruning loppers. A killing cone can be made from many different containers or materials you night have on hand. Some people just break the neck using their bare hands. You should have something already on hand you can use to kill a chicken if you learn the technique.
My work table is two 2x8's set up on sawhorses I already had. I use a hose with a control head on it to control water. I already had that.
You need a knife. You read a lot on here about how it has to be sharp. It really doesn't "have" to be that sharp but sharp makes it a lot easier. Sometimes if you are looking for "cheap" you have to work harder. When I was a kid I'd use one of Mom's kitchen knives which wasn't always that sharp but then I was only butchering one at a time. When I grew up and started butchering several of my own for the freezer I got a knife with replaceable blades so I could keep a sharp knife. Sharp makes it a lot easier. If you learn how to sharpen a knife you should have a knife in your kitchen you can use. I use poultry shears for some cuts so I don't dull my knife. My wife already had those.
My wife wants then skinless so I skin when I butcher, no need to heat water. When I was a kid mom wanted the skin on. She was feeding five kids plus the adults so she wanted all she could get. She wasn't worried about how pretty it was, but she wanted the skin. She did not use the feet but some serving pieces were liver, gizzard, neck, and back. Instead of boiling a pot of water to a certain temperature and dunking she'd bring a sauce pan of water to a boil on the kitchen stove and I'd pour that over the bird, then pluck it. That was probably pretty close to dry plucking but I had young hands.
To hold the meat and cool it down after cleaning I use an ice chest I already had and filled it with ice water. I typically do about 5 to 7 at a time. I make extra ice in the freezer ahead of time and use that so I don't buy ice. After I finish I wash everything down and sterilize everything non-metal with a bleach solution.
I dispose of the offal by digging a hole in the garden in an area that won't be disturbed for a couple of months at least. I don't know what kinds of costs you may have in getting rid of the offal.
I don't know how you plan to store them in your freezer. If you use a zip-loc bag you have limited storage time before you get freezer burn. Some people use heat-shrink bags or vacuum bags. I use freezer paper and freezer tape and double wrap them, they last a long time. I freeze mine in parts, not a whole carcass. I don't know how you avoid spending some money on this.
There are trade-offs in everything. You may need to balance cost, schedule, or quality. I bought the knife to make my life easier. I buy the bleach to sterilize things, and the wrapping paper and freezer tape. I can't think of anything else I bought or buy to butcher chickens, I use what I have on hand.
