Kudos for wanting to start learning.
A plastic shed will only last so long and then you can't repair it. And, it's plastic. Build it with wood etc. and you can fix it, build it how you want, and at the end of it's life it can be used as fuel or composted.
Hammer yes, small nail puller, nail set set, utility knife, speed square, $4 tape measure with scratch-pad stuck to the side (can be moved to next one). 2' level. Folding sawhorses.
Power tools: circular saw to start, jig saw, chop saw to follow. A smallish compressor to run a nail gun (a framing gun will come in handy for the garage) is a good investment.