I built the cage below with very few tools. Not because I didn't have other tools, but because I wanted to teach a friend how easy it was to build a cage with just very basic tools and construction techniques.

I may have used a miter saw on the trim around the face, although even that's not necessary since the trim is not necessary.
Otherwise, we used:
A cordless drill with a pre-drill/counter-sink bit and a square drive screwdriver bit. I really would not want to build a cage without these, although it could be done.
A caulk gun when I attached the glass track. But you can also buy adhesive in squeeze bottles, meaning no caulk gun needed.
Cheap foam brushes to apply the stain and polyurethane. Even these are not necessary as you can often use an old shirt to apply them. The interior epoxy was poured on and trowled around with a scrap piece of cardboard. Now that I think about it, we also used a 24" level to make sure each panel was flat and level before applying the epoxy. Again, not absolutely necessary.
I believe I also used my circular saw and an edge-guide to clean up some of the cuts I had done at Home Depot.
With hindsight, I think it's worth paying a bit more to have the cuts made at a quality cabinet shop. Not only is the plywood and melamine they carry of much higher quality, but their cuts are absolutely perfect. This makes a noticable difference when assembling the carcass.
I do find a circular saw and a 4' edge-guide are invaluable, but for just a few cages I don't believe they would pay for themselves within a few projects, especially since I would recommend an expensive circular saw blade. If you do go that route, you'd also need a tape measure and a carpenter's square.