you can start with this link, to find out what method you would prefer. I also attached two papers mentiond in that link. So you can , for example, pick one of those methods to prepare your competent cells.
It could be a nice experiment to perhaps try both methods (make cells competent with both methods), then transform with a plasmid and check for the efficiency.
And store competent the cells in -22°C and redo the transformation every week and check how the efficiency is influenced by the storage time...
This is just a simple project (also pretty cheap) to start with.
Perhaps you can do it with more than 1 type of cells: eg. E. coli top10, E.coli dh5alpha, and...
it could already be a nice experiment and its pretty easy and cheap to try/do.
All you need are the cells and the plasmid!
(and the reagents of course)