Probably your best option would be a couple of fill stage lights to give an overal good lighting, and then, because I'm sure there will be some inside and underside shots, you'll want something more portable as well, there's some phone rigs that give you hotshoes for portable lights and portable mics.
I'd say stock up on a couple of lights, a number of GoPros, I'd have a go-pro above your work space, and 2 in either corner of your garage to give you camera angel options and they'll give you a nice wide field of view. Ad a more regular camera (go-pros aren't always fantastic video quality, they're mostly used for their robustness and wide angel, bands and artists use them, gopros are designed to get dirty)
You could even get by with some construction lamps. I've used construction lamps in the past (same ones they use on renovation sites, small portable, and now that they're mostly LED, you don't have the same overheating problems)
Maybe look into some coloured LED lights so that your area isn't overlit and boring, add a little flair, and then when you're filming with everything, just be sure to make a loud enough noise the sync up all the cameras.
Auto channels don't need the best visual quality, but you do want some cameras that will cover both wide shots, and close up shots. Go pros are great for pretty much all that, and your phone will do a decent job as well. Then make sure you have a decent mic to pic up your audio. Probably a lav mic would be best so you always have the mic close to you and you don't have to worry about holding the mic when you're working on your vehicle.