People actually invest more into bitcoin before halving because after halving that is actually when the price is low because after halving there is bull run.
People invest massive and more after bull run. If people are not investing after bull run, the price of bitcoin will nit increase. The bulls means that their are more people that are buying.
An old desktop or laptop if you have will be enough. The important thing is to download the official wallet of Electrum from its official website because too many clones and fake out there.
Yes an old computer is good in a way that you will remove the wifi and bluetooth modules. Sparrow can also be used, it is a good bitcoin wallet.