Yes, you might want the highest precision possible - for example when you build furniture which benefits greatly from precise cuts. The most convenient way would be to draw the line that will signify the edge of the piece you want cut so that the blade cuts the line and whatever material is on the far side of the raw board. Something like this:
|the detail you want|line|remaining material|
| |blade cuts here|
This is quite easily achieved with power saws even without a guide and will be more of a challenge with hand saws.
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.
Best Answer
The advice is good in the other answers too. Your blade has a build up on it that will cause the blade to wander, typically from heating up and distorting, very difficult to cut a straight line with that happening. Do invest in another blade. I also use something on the face of the door, like thin cardboard, taped down, or tape the bottom of the saw so the metal base does not leave marks on the painted door. Another way to insure no tear out, is instead of marking with a pencil, carefully score the cut line and cut along that. With the new blade stay just a hair's width away from the score line, and when finished the cut, wrap a piece of medium to fine grit sandpaper around a block of wood and sand the corner only, holding the block at a 45 degree angle while sanding to ease the corner a little. This help keep the edge from chipping while resetting or from something getting caught under the door while opening and closing.
To answer the question about correcting the over cut, yes just shift the line the amount to need to incorporate the over cut into the re-cut.
The saw blade that would be good for all around use, and get the nice cut you need would be a carbide tipped blade between 24 and 40 teeth. I would determine which blade for you by what do you plan to use it most for. If it is general cutting or ripping the 24 tooth will do fine, even for cutting the door bottom. If you plan to do more with finished material, then the 40 tooth is a better option, although it will do general cutting just fine as well