As for background:
First off, my father was a mechanic most of his life. He grew up modding musclecars for 1/4 mile tracks and general mayhem during his high school years. Poor family in south texas, small town, etc. It's easy to fill in the cliche picture
Now he's a bigwig at a major oil company, but he worked his way up from working in their maintenance shop on deisels. As you can imagine, my childhood was filled with hanging out in the garage watching my dad do maintenance on the family car, and restore random project cars that were constantly traded off for new ones. I learned a lot from him. My first few car projects on my own, he was my go-to resource when I ran into things I couldn't figure out, but these days I rarely have to bug him anymore, although I still consider his opinion invaluable sometimes.
Professionally, I'm a computer programmer/engineer/hacker/ whatever-you-want-to-call it. It's really the same kind of brain activity, just different specific field of knowledge. I draw a lot of mental parallels between hacking on cars and hacking on source code (and hacking on everything else around me).
If you're coming from not working in any kind of related activity and have no background knowledge to draw on, mechanic stuff is actually pretty hard, and it's pretty easy to get yourself into a mess you can't fix, so be cautious in what you take on. As for learning: your best bet is to start making friends with mechanically-inclined people in your area. Once you find them, hang out at their place on the weekend and help them out on projects and observe, etc. Then get them to help you out on yours
Tools get quite expensive in the long run. A full suite of quality tools could run many thousands of dollars, and is generally something you slowly build up over time. I really like buying my basic hand tools at Sears (Craftsman), because they come with a lifetime warranty. If you break a socket or a wrench, you can take it back to any Sears anywhere and get a replacement. However, there are plenty of good tool companies out there, and you'll find lots of differing opinions on that stuff. Just don't go for the ultra-cheap $13.99 socket set from AutoZone that comes from a no-name manufacturer. They're made from cheap cast metal, and you will break those regularly doing any real work, and they won't replace them.
(Actually, just to contradict myself, sometimes I buy cheap sets too, just to have throwaway tools for in-car emergency kits, or because I know I'm going to intentionally grind down a tool and customize it for one job and I don't care if it breaks, but that's a whole other matter).
So, for the super basic list of tools, here's a good starting point:
A decent pre-packaged socket set in 3/8" drive (they come in 1/4", 3/8" and 1/2" drive commonly). For the Z, everything is metric (mm sizes), but it's nice to have standard sizes on hand as well (fractional inch sizes) if you're building out a set of general tools. This socket set should contain at least a 3/8" drive ratchet, and a set of basic sockets ranging from say 8 to 18-ish mm at the minimum.
A half-inch drive socket set could come in handy at times too, it allows more force to be applied on bigger jobs. Generally you won't need small sockets with it though, you're looking for sockets more in the range of 14 -> mid 20's mm on the half-inch drive. For really hard bolts (like our crankshaft pulley), you'll want to buy large breaker bar in half-inch drive, which will fit these sockets as well (a breaker bar doesn't ratchet, it's simply a giant long handle that can attach to sockets).
You'll also want some combination wrenches. These are the basic non-mechanical flat wrenches with a closed ("box") end and an open end. You may want to pick up two of the more common sizes, as you may need to use a pair of the same size together on some jobs.
GearWrench-style wrenches are really hand too (they have a ratchet built into the box end, but otherwise look like plain combination wrenches), but you still need the plain ones as well. Gearwrenches alone are not a good substitute for the plain ones at times.
A quality torque wrench or two (1/2" drive and 3/8") is essential for many tasks as well, as it allows you to re-tighten bolts to precision levels of torque. As you become more experienced, you don't use it as often on "less-critical" bolts when you think you can guestimate pretty close by feel, but knowing which torque values aren't very critical and having a feel for torque values is something that won't come for a long time.
A prepackaged set of several flat and phillips screwdrivers is also a must, as well as a few good sets of various kinds of pliers (needle nose of a few different sizes, locking, slip-joint, groove-joint being among the common ones).
Of course, for working on a car you'll also need equipment to lift it. This means a low-profile floor jack, a set of 4 jack-stands, and an extra bottle jack or two can be handy at times as well. Be sure to check the ratings on these, to make sure they can hold the weight of the car reliably. Never work under a car supported by just jacks, as the hydraulics could let loose without warning (not to mention they're on wheels in the floor jack case). Just use the jack to get the jack stands into position, then remove the jack. Be sure to get some wheel blocks too, to block the wheels from rolling while you're jacking the car up.
From there, the list starts getting a whole lot longer, more expensive, and more involved, but just getting the above will get you started out. Expect to have to make lots of last-minute runs back to a tool store in mid-project to buy more tools you're missing as you go though (so have a backup car to do that in while your car is on jackstands).
I'm sure I'm forgetting a million things too, it's hard to summarize years of aggregated tools and info into a random off-the-cuff posting
One thing that's nice about tools on the 370Z: For 95% of all tasks, all you need are 10mm and 14mm sized tools. Virtually everything is one of those sizes, although here and there I've run into a few 12mm, and the crankshaft pulley was either 19mm or 20mm, I forget which.