The following woodworking tools are listed in order of importance.
1. Circular Saw
While some people consider the circular saw to be more of a carpentry tool than a fine woodworking tool, I would tend to disagree. There may be no more versatile basic handheld power tool than a circular saw. When used with a clamp-on straight-edge, the circular saw can be just about as accurate as a table saw and handle quite a few of the tasks that one would attempt with a table saw, particularly cutting sheet goods such as plywood or medium-density fiberboard. When woodworking on a budget, a quality circular saw should be the first handheld power tool purchased, as it is the one that will likely be the most useful as you get started.
2. Power Drill
Some might expect to see a cordless drill on this list, but when we're talking about basic power woodworking tools, a corded drill is more versatile and powerful. Sure, the cordless is, well, cordless, which makes it more portable, but corded drills are less expensive and can do more than a cordless drill. There are some options to consider when choosing a corded power drill, such as whether you want a 3/8-inch or 1/2-inch chuck, keyed or keyless chuck, straight drill or hammer drill, and so on. Learn all about these options (along with some suggestions on what to look for when shopping) in this article on corded power drills.
The fourth most important basic handheld power tool every beginner should buy is a random orbital sander. While palm sanders are less expensive and can use plain sandpaper (cut into one-fourth sections), the random orbital version uses hook-and-loop fastened sanding disks, and doesn't sand in patterns, using instead a random sanding motion. This will motion will serve to reduce the chance that any sanding marks may appear on the stock due to the sanding. Of course, be certain that your local woodworking supplier has sanding disks readily available in a number of grits to fit the model that you choose, as the key to proper sanding is to use progressively finer grits as you sand to reduce or remove any marks that are left behind from the previous sanding.
5. Table Saw
Once you have the four aforementioned handheld power tools in your arsenal and you've had time to get comfortable with using them, its time to make your first (and likely most important) major tool purchase. The table saw is the heart and soul of every woodworking shop, the centerpiece around which all of the other tools are used and organized, so you'll want to buy the best table saw that your budget can comfortably afford. Take the time to learn which features you really want and the table saw that best fits your budget and your needs. This article will show you the most common features, and how to determine what features you need and how to know if those features are really well built, or simply added on to the saw because they are selling features.