Any inexpensive digital meter will do fine for checking voltages and continuity. $10 on eBay.
ebay.com link: NEW Digital LCD Multimeter XL 830L Voltmeter Ammeter Ohmmeter OHM VOLT Tester

I've got that exact one, works just as well as my $120 Fluke meter.

Just take your time and do a lot of reading. If you feel unsure or uncomfortable about doing something, stop right away and do a little research on it. It isn't worth the work to undo a serious mistake. There are plenty of good instructional videos for all of this stuff (as well as bad ones too), but for the most part, you can learn the basics fairly quickly. And everyone makes mistakes and screws shit up from time to time. I see from your posts you're not afraid of that, which is a good start.

It isn't as complicated or intimidating as it seems if you just break things up into smaller chunks. I've been tinkering in electronics for about 15 years now, but it only took a year of little projects here and there to understand all of the basics. The rest was just learned while I was working on a variety of different things.

I started with guitar effects pedal building, which is a great way to get into this stuff and is extremely simple. You also get the instant-gratification factor of building a working effect in an hour or so.