So you'll need that bottom bracket removal tool and a crank puller. If you're working on bikes a lot, especially older and budget rides, you'll use it a lot. If your replacement bottom bracket is an external style - like if you got the popular budget option, the IXF crankset and bottom bracket, you might want the external BB tool. You can probably install it without, though.

Side note: I have the separate BB tool and crank puller, but in my searching I see this combo set that may work. It certainly is less money.

Good luck. This is a good project to get your feet wet with some upgrades and these required tools can see a lot of work.