As with anything, you can spend as little or as much as you like.
Having a table saw is a major plus, although you could get away with a hand-held circular saw, and straight edge, such as some metal tube to act as a straight guide to run the saw against.
You need to decide how to make the corners - comb joints, (finger joints) not sure what your US term is, require a lot more equipment, typically a router, and a finger joint jig, or you can cut finger joints on a tablesaw.
If you are going for simpler construction, you can either joint the sides with nails, or screws - screws would be preferred. They last longer. I'd glue everything with outdoor glue as well. You could use a biscuit jointer to make the edges, but I suspect it wouldn't be anything close to as resilient in the long term, and susceptable to breaking even, if the hive was full.
Although it sounds obvious, a good square is essential to ensuring everything is made up accurately.
If you want to do slightly more sophisticated work, a router is useful for making hand-holds, rebates etc.
Just my thoughts.