From a "size - only" standpoint two critical dimensions of a bandsaw are the throat capacity and the maximum cutting height.
- Throat capacity is the size of the opening between the blade and the frame. You need your workpiece to be able to fit through this opening as you push it through the blade.
- Max cutting height is the maximum amount of blade that can be exposed. This will impact how many pieces you can stack. Keep in mind you may not be able to fill the space, depending on the material.
Larger, more expensive bandsaws will generally have better blade guides, a more powerful motor, more table and fence adjustments, and can hold wider range of blade widths. Adjustable speed is nice if you intend to cut metal, as slowing the speed will increase blade life.
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
It's a gimmick.
Since proper tooth size on a hacksaw is directly related to the thickness of the metal you are cutting, you are guaranteed to have 2/3 of the blade be the wrong toothing for whatever you are cutting.
Save your money to buy a better quality hacksaw frame that you can easily and quickly switch blades on, or get additional hacksaw frames and keep different toothed blades mounted in each one.
There is a different product of the same name that has some benefits in some situations - a "Variable Tooth" which is more of a slight variation (like 17-18-19-18-17-18 instead of 18) to reduce problems of harmonic vibrations from an interaction of tooth size and sawing speed. This is not the product you asked about, and it's of limited benefit for hand hack sawing where the user will simply adjust speed to avoid the vibrations.