What tools do I need for this

I want to replace the crank and bottom bracket on my commuter bike. It’s a very old Trek 330 steel frame. The crank is some kind of plastic/resin, and underneath the dust caps there are bolts with a close clearance to the sides. On the left hand side of the BB there’s a ring (cup? is that what it’s called?) pressed against the frame, with I think 6 notches, and on the drive side there’s a same looking ring but with no notches. I’ve seen some tutorials online for the process, but I’m a bit confused about the lack of notches on the right side, and the holes in the cranks don’t look big enough to fit a socket to remove the bolts in there (I don’t have a socket set to try though).
So no tools, and I don’t have a crank + bb setup picked out to replace it yet. Clearly I’m a newbie at wrenching. How do I do this right?

The crank bolts can be removed with a crank bolt wrench. Yep, it’ll fit the small clearance.

The cranks will be removed after the bolts are out with a crank puller.

The bb non-drive side 6 slotted “nut” takes a spanner wrench.

The bb drive side will be removed after the non-drive is unlocked as stated above, with a bb wrench.

All these tools are specific to bikes and can be bought at your local bike shop.

Its fun working on your own bike.

The Park Tools website has excellent instructions for almost any bike repair you can imagine.
I think this link explains everything you need, including the necessary tools and how to make the final adjustments.

I’ve seen some tutorials online for the process, but I’m a bit confused about the lack of notches on the right side,
Once you’ve pulled the right crank arm, you will probably be able to see that the inside edge of that cup is splined. There is a special socket that will fit it.

So trying to list the tools I need (links to park tools):
Crank and BB wrench
Pin spanner
Socket set
Crank puller
Wrench

Sound about right? Also, when shopping for a replacement crank+BB, how do I make sure that they’ll work with my frame? I’m looking to get a track crank for a single speed conversion, if that makes a difference.