As far as books, I highly recommend The Complete Book of Woodworking: http://www.amazon.com/The-Complete-Book-Woodworking-Detailed/dp/1890621366/ref=sr_1_1?ie=UTF8&qid=1335885982&sr=8-1. It's easy to follow even for the uninitiated. It goes over the major tools, what they are used for, and has excellent instructions on some starter and intermediate projects. There are even some workbench projects toward the end, one of which is made only from plywood and 2x4 lumber. I made it with a jigsaw and really uneven cuts, and it's held together well for about a year (it's usable for everything except hand planing). I'm also a software engineer by trade and learn well from books, so I spent a good few months obsessing over this book in my apartment before buying a house and really getting started.
For video instruction, The Wood Whisperer is one of my favorites; he gets into what tools are used for, how to set them up and tune them, and has some videos dedicated to safety. He's also very technical and comes from a science background, so the engineer in me relates well with him. He doesn't leave out many details. Fine Woodworking is also very good and for $5 a month you can get access to a ton of video content.
http://www.thewoodwhisperer.com
http://www.finewoodworking.com
SawmillCreek and WoodworkingTalk are nice forums to search through for tips and discussions about what tools are best used for what projects.
http://www.sawmillcreek.org
http://www.woodworkingtalk.com
Most of these will discuss fine woodworking, furniture making, and detailed joinery, which you may or may not be interested in. All of them, however, will give you information you want about tool usage. It may be more detail than what you're interested in for the projects you describe, but if anything you'll be over-prepared.
Use a router with a plunge base and either an edge guide or straight edge, depending on the size of your work piece. Attach stop blocks to the workpiece and/or straight edge (clamps would be one easy way to hold the stop blocks in place). The stop blocks will prevent you from cutting your slot too long. First set up the edge guide or straight edge with the appropriate offset for your router base, parallel to where you want the slot. With the router unplugged and the bit almost touching the wood, position the router bit where you want the slot to start. Then use the router base to gauge exactly where to position the stop and clamp it in place. Do the same for the other end of the slot, then proceed with plugging in the router and cutting the slot in several passes, going slightly deeper each time.
You can also use a router table to do something similar, but the steps for setup will be different since you won't be able to see the cut as you're making it. However, you will be able to use your router table's fence and possibly other T-track or miter track accessories.
Although your material isn't very thick, it's still not a bad idea to cut the groove in multiple passes.
In a pinch, you can also use a Dremel/rotary tool (which is essentially just a tiny, low-torque router) along with a router attachment and multipurpose spiral bit, but a router will give you slightly better results.
If you don't have a router, it's relatively easy to cut this slot by drilling a series of overlapping holes with a drill press and Forstner or brad-point bits, then clean it up with chisels.
No matter what solution you use, be sure to put a sacrificial piece of scrap wood on the back side of the workpiece to help prevent blowout when you cut all the way through to the other side.
Best Answer
One of the most important things about making a stool is getting the legs the same length. I would suggest you modify the miter box something like this:
Keep everything square when building the stop piece. Then when you actually go to cut the legs, butt a square end to the stop, clamp it down, and cut. You will get three or four legs precisely the same length.
Keep the stop piece. You can move the stop around easily, and you will use it again.
Time spent making a jig or a stop is never wasted.