Resurrecting an old car is an awful lot of fun, and it's true that old cars are an order of magnitude less complex- no data buses, ECUs, ABS malarkey, etc but it's also a gigantic commitment of time, money and space. You'll need lots of tools, at least one garage, a big parts budget, and a lot of free time, and if the car needs any welding work then the costs, scope and difficulty of the project goes up hugely.
If you decide you do want to go down this route, I'd thoroughly reccomend going for a 1960s/70s British type as spares will be cheap and relatively easy to obtain. If you want a saloon, look at Minis, Minors, Austin A30s, Hillman Imps and the like. If you want something more sporty have a look at the MG Midget/B and the Triumph Spitfire/GT6 as a starter.
I started messing around with cars when I bought a long-dead 1960s convertible, and now a year on it's only a few more weekends away from an MOT. I also do my own maintenance and repairs on my 21st century runabout. I am fortunate however to have a knowledgeable Dad with a garage full of all sorts of weird and wonderful kit! I'm moving out soon, so on my last birthday my Dad bought me the start of my very own tool collection in a thoroughly emotional man-moment.
If you just want to get into understanding and working on cars though I'd suggest starting with a cheap but working one and a Haynes manual. Learn about the principles of the major systems- electrical, ignition and timing, brakes etc alongside learning how to work safely lifting and supporting the car, disconnecting the battery and so on. Start with small, basic maintenance and repair work (say, changing the spark plugs, oil and brake pads/shoes) and gradually gain confidence. Remember that seemingly simple jobs in the manual can in reality turn out to be awkward, difficult or dangerous in reality, so check out the parts you'll be working with on the car thoroughly before you start wielding spanners, and don't take anything apart unless you're absolutely sure you can put it back together in such a way that it will do it's job safely.
Equipment-wise, as a starter I'd suggest some of the following:
-Good quality spanner/socket set
-Good quality screwdriver set
-Pliers
-Feeler gauges
-Torque wrench (if you plan to be working on major bits like the cylinder head or the manifolds)
-Hammer (and a rubber mallet for precision adjustment of rubbish British Leyland parts)
-Cable ties (x 500,000)
-Mulitimeter
-Cheap and cheerful fault code reader (for a modern car)
-Copper/bearing grease
-WD40
-Hydraulic jack and axle stands (or ramps)
Also, disposable latex gloves have saved me from nasty chemical burns many times.
It's a lot of fun and a lot of satisfaction to learn how to work on cars, so best of luck and hope this helps!