Which tools should everyone have in their home garage?
These are the fun questions to answer 
first off, toss out those cheap socket wrenches. They’re gonna break halfway through a job and infuriate you.
One important thing to remember is not to get seduced by the Snap-On truck. They’re great tools, but they’re also overpriced beyond belief. I only get Snap-On when they’re literally the only company that makes a tool I need, and that’s pretty rare. The exception to this is garage sales. A lot of times people will be selling stuff at insanely good prices. Start working garage/rummage sales, etc watching out for Snap-On, Matco, and Craftsman.
Here’s a list of tools I consider essential:
Hand tools:
A GOOD 1/2 inch drive and 3/8 inch drive socket wrench. Craftsman is fine (even the new, non-made-in-USA ones, despite what some will tell you). If you want to splurge on a 3rd socket wrench that will make you happy every time you use it, get a Stanley rotator ratchet for around 20 bucks. You can twist the handle back and forth to drive the ratchet head. Don’t use it to break bolts loose, but if you’re working in a tight area, being able to twist rather than trying to lever a ratchet around without hitting stuff is much easier.
A GOOD full set of metric and a full set of standard sockets. Cheap ones can break under too much torque or round off the bolts, both of which will infuriate you.
A good set of metric/standard deep-well sockets.
1/2 inch and 3/8 inch extenders, both short and long, for those hard to get at places. Also a u-joint for the socket wrench is nice, for reaching bolts that you cant go at straight on.
A clicker torque wrench from Harbor Freight. Cheap, just as accurate as the expensive ones, and necessary for a lot of engine work (head bolts, etc) and even just for rotating tires. Remember to store it at 0 foot/pounds so you don’t crap out the spring.
While you’re at Harbor Freight, pick up 3 or 4 magnetic parts trays. Much better than casting about under a car trying to find that bolt you put down and then kicked aside when you moved.
Also at Harbor Freight, get a telescoping magnet pen. When you drop a bolt somewhere in the engine bay, you just extend it and pick the bolt up with the end rather than trying to worm your fingers around in tight spaces.
A GOOD set of screwdrivers. Craftsman has a good one for around 40 bucks that has all you’ll ever need plus a storage case. Cheap screwdrivers strip screw heads and infuriate you.
A screwdriver magnetizer/demagnetizer. 99 cents or so. Makes it easier to install screws if they’re not constantly falling off the end of the screwdriver.
A thor hammer! Also known as a short-handled sledge hammer. You’ll use this to pound off rusted parts. A deadblow hammer also comes in handy.
A GOOD metric and standard wrench set - some bolts will be in spaces that are too narrow to get a socket wrench in.
Air tools:
A decent compressor. For your purposes, a 20 gallon one from Home Depot (or if there’s one in your area, a Sanborn one from Menards) will do fine. Try to avoid oil-less compressors. They’re too loud and will wear out faster.
At least a 20 foot air hose.
A quick release system. This lets you pop tools on and off the hose rather than screwing them in with fresh teflon tape each time.
A decent impact gun. Don’t get the cheapie $20 Coleman here. If you want to save some money, get the Earthquake one from Harbor Freight. You want something with some muscle to it.
Air sockets. Do not use regular sockets with an impact gun. They can shatter.
A tire chuck. For filling tires.
An air chisel. These come in handy for things like blasting frozen rotor screws off when you’re doing a brake job.
Ear protection. Chisels are loud.
Jack-related stuff:
A good floor jack. Costco sells a very* good Arcan 3.5 ton jack. If you’re not a member, Northern Tool has the same thing for something like 40 bucks more. Don’t cheap out here and get the little Home Depot special.
At least 4 high-quality jack stands rated for more than you think you will put on them. If your heaviest car weighs 2 tons, get at least 3 ton jack stands. Use them every time the car is in the air. Jacks cannot be trusted to hold the car, and if the jack fails while you’re under it, you’re very likely to die. Don’t even think about cheaping out on this one. I say at least 4 because sometimes you’ll have a car up on all 4 for a long term project, and your other car will break, and you need to fix it. 2 more come in handy there.
2 wheel chocks. Harbor Freight sells a good little metal folding set with rubber feet. Use these when jacking up one whole end of a car so that the other end doesn’t start to roll.
A creeper. This makes life a lot easier if you’re sliding under the car a lot. You can cheap out on this one if you want, but if you want a nice one that you don’t have to worry so much about your sleeves getting caught under the wheels, get a Bonester. That’s pretty expensive, though, and a $30 one from Harbor Freight or Home Depot would do you just fine.
Misc:
An oil drain pan. Useful for catching all kinds of fluids and storing them for disposal.
A bag of Oil-Dri. It’s basically cat litter without the odor eliminators. Use it to soak up fluid spills that you did not catch with your drain pan.
A rolling magnetic pickup tool. Use it to find all the stuff you lost during your project.
A shop broom.
Lights. Lots of lights. A twin-headed shop light on a tripod ( http://t1.gstatic.com/images?q=tbn:ANd9GcTSswM24xjVRrrYntWKsvMo0fFIgXOcQVVxfRFAOebHSZld--TrhA like that)
An LED headband light. You can find them at Harbor Freight cheaply. Get a couple. You can never have enough light. Get the one that detaches from its headband and has a magnet on the back so you can stick it in the engine bay as a steady light.
Safety glasses. Lotta grit dropping into your eyes when you’re under a car.
Non-essential, but nice to have:
An OBDII reader. If you have an Android smartphone, you can get this on the cheap. Get a bluetooth OBD2 reader from Amazon for around 25 bucks. Then get Torque Pro from the app store for something like 5 bucks. You’ll have 90% of the features of a real reader that costs 100’s of dollars. This will allow you to read fault codes, which helps you diagnose problems.
An air ratchet. Basically like a hand ratchet, but air powered. Makes things go on and off faster.
A dremel with a flexible shaft extension. Very handy for cutting and grinding things.
A pop rivet gun. This is a really cheap tool that you can use to fasten almost anything to almost anything else. You just drill a hole, stick a pop rivet in it, and squeeze the tool for a solid connection. I like these better than nuts and bolts in many applications because nuts and bolts can vibrate loose without a lock washer or locktite. Pop rivets won’t come loose unless you drill them out.
A tool chest to hold all that crap. You will probably eventually want a big rolling tool chest, because keeping all that stuff in small tool boxes is untidy and makes it hard to find things. Hold off getting one until you get to Maine - a good one is very heavy and tends to cost a lot of money to move. I personally recommend Masterforce, as it’s almost as good as Snap-On, but $800 will buy you what you’d pay at least 5 grand to Snap-On for. You might not be able to get that where you live, though. It’s a Menards exclusive brand. I recommend against Craftsman. They used to be really good, but they’re making them much cheaper now and they’re overpriced junk.
A rolling cart so you don’t have to keep pacing back and forth between the car and the tool box.
A work bench with a vise.
A drill with good bits.