For the base, you will need wood glue, masking tape, sandpaper and finishing supplies.
For the kit, finishing supplies will largely depend on what parts you may wish to finish. I usually like to give the chassis plate a couple of coats of something clear, but you may want to do more. The transformer bell end usually needs some attention with steel wool and some kind of finish, as it is pretty much just plain steel and prone to the usual rust.
To do the assembly and electronics, you will need soldering stuff, a multimeter, and hand tools. The hand tools list can be as big as you want to make it, if you're a tool hound like I am, but it can also be pretty minimal: Screwdrivers, needle-nose pliers, wire cutters, and wire strippers are essential.
You will need a place to work with plenty of light. It is also nice if your work-place can remain undisturbed between sessions.
Finally, it is always a good idea to have some kind of eye protection when you are working on anything. Using a diagonal wire cutter can result in pointy little snips of wire shooting out at high velocity, as one example of hazard. There are others.
Also in the eye department, a magnifier of some sort is pretty much required to identify the smaller parts, and is very useful in inspecting your work.
Again, you may want to add endlessly to your tool supply, if you're like me; I think of something new I'd like almost every time I work on something! But, you don't need a Sears in your basement to assemble a Bottlehead kit.
