As a beginner in the DIY world, you will need tools for cutting things apart, and putting things back together. In addition, you will need tools for finishing touches and clean-up.
Cutting Things Apart
A circular saw is a good investment. It's good for long, straight cuts and will work faster and more accurately than a jigsaw. Look for safety features on this saw -- paying a little more for your safety is worth it. Some circular saws can be adjusted to do a 45 degree angle cut, and are available in corded and battery type. As with any power tool, the corded version will be the most powerful, least expensive, and won’t give out on you in the middle of a project.
When I first started doing things for myself, one of my first tools was a jigsaw. I wanted to build a bench for my parents. A table saw would have been a better choice, but being a beginner and a little tight on funds, a jigsaw was better than a hand saw. A jigsaw can do straight or curved cuts, which makes it one of the more versatile saws. One of the best jigsaws for beginners is the Black and Decker JS660 (according to Best Reviews). It does not have all the fancy stuff an expensive jigsaw has, but is easy to use and is just right for the beginner.
Putting Things Back Together
Everyone knows what a drill is, so I won’t go into much detail on that. They are available in battery-operated or corded versions, but drills with cords are less expensive and usually have more power than their battery-operated counterparts. Lithium ion battery portable drills are widely available and have been coming down in price -- they're the most versatile option for any drill. However, lithium ion batteries do not give you any notice that they are running out of power -- they just quit when the battery is exhausted. If you are like me, you absolutely hate running out of power in the middle of a project so make sure to purchase a set that comes with two batteries and a charger.
A cordless screwdriver is not a must, but it sure is nice to have and they are not very expensive. I like having the screwdriver as a separate device because I hate changing my drill back and forth from a drill to a driver. Keep in mind that a cordless screwdriver is only meant for driving screws in pre-drilled holes. You can use it for light drilling or driving screws into softer wood, but it won't be as powerful as your drill.
For bigger projects, a belt sander is a must-have. Belt sanders can sand a floor or a cabinet door and they are easy to use so they suit the beginner well. Most models have a variable speed adjustment, so you can fine-tune according to how delicate your project is.
Any wood project will require some finishing touches, which will involve sanding! My favorite and most versatile for small projects is the mouse sander. I believe it got its name because of the shape of the sander. It fits in the palm of your hand and the sander is pointed like a mouse nose. I like the pointed end because I can get it into tight corners, and use this more than any other sander I own.
Odds and Ends
Although not really power tools, there are some things that every workshop should have. One is a good shop vac for cleaning up dry and wet messes. The other is a good work light. You need to see what you are working on, and the best way to do that is with good light. Don’t skimp on these two things -- you will need both for many years to come.