Drill Press:
I use a very inexpensive tabletop model and get acceptable results. A useable drill press can be bought for around $100 or less. You could try making a joint with a hand drill, but I doubt that it would work very well.

Drill Bits:
5/64
7/64
1/8
3/16

Metal File:
I really only use one good file for everything.

Hacksaw or Dremel Tool:
Hacksaws are inexpensive and work just fine.
The Dremel tool fitted with a cut-off wheel makes things a little easier.

Brass Stock:
1/4" by 12" (for the 1/4" ball joints)
1/2" by 12" (for the 3/8" lamp ball joints)
Get this in the small metal stock area at the hardware or hobby store.

Threaded rod, screws, nuts:
I mostly use 4-40 threads for balls, and the screws that hold the plates together. For the smaller balls I use 2-56 threaded hardware. Brass would be best if you plan to solder the balls to the threaded posts.

Thread Taps:
Tap handle tool
4-40 thread tap
2-56 thread tap

Bench Vise:
The simple bench vise that I use cost under $20.

Small Clamps:
You can use 'C' clamps, spring clamps, vise grips... whatever will hold the strips together for drilling.

Locktite (or) Solder:
If you are going to get Locktite, get the red stuff (#27100). The blue is not strong enough. It is also possible to use Superglue, but I don't recommend it. To solder balls to threaded rod, I would recommend a rosin core solder and a propane or butane torch.

Permanent Marker:
Fine-tip Sharpie.

Here are some extras that you don't really need to make joints, but they may make your life easier:

Drilling Jig:
I made my jig out of a plate of metal and some aluminum bar stock. Here is a scale picture. The purpose is to align the two strips of brass and keep the proper orientation. The jig also has marks on it that I use to drill holes in the right places. It makes 2 drilling operations alot easier, but you don't really need to have a jig to make joints. Sometimes I don't use it.

Stationary Belt/Disc Sander:
You don't really need this, and I've only aquired mine recently. It sure makes the job of cleaning brass edges easy, though.

Cutting Fluid:
I used to just use auto oil as cutting fluid. I've found that for the simple drilling, shaping, and tapping that I do, no cutting fluid is really needed.