An oscilloscope yes, but also a an isolation transformer. That will greatly reduce the chance of a fatal accident if you touch the wrong thing
this is just about the cheapest scope you could get any use out of. You still can't do high voltage without differential probes, but you would need to buy those separately with more expensive scopes as well
also, get yourself
one of these types of devices to do a quick check on diodes and transistors. It's not completely foolproof, but I find they generally don't lie, and they will almost certainly tell you if a transistor is still showing as one or not. Capacitance is also fairly accurate up to a certain point. I think they start to get so-so around 2200uf and up
I'm not specifically endorsing either of these two devices or sellers; there are many versions of them on amazon and ebay, and they are all pretty much the same thing AFAIK. Just read feedback and stuff and find a good deal on a good one