Before I started the Cocktail Cabinet, I hadn't done any woodworking since high school (and that was a long time ago). I've been building up my workshop, and here's what I've learned about what you need:
Your Power Drill will be your most used tool. It's useful for both drilling holes and also as a screwdriver. Go for a cordless drill. You want two batteries, so that one battery is charging while the other is in use.
My personal drill is a Black and Decker 12 volt FireStorm. One nice feature of this drill is that the chuck that holds the bit can be removed to reveal a socket for a screwdriver bit. You can easily go from drilling to screwing and back without having to refit your drill bit.. I often use this feature by drilling one hole, putting in the screw to hold things in place, and then drill the other holes.
Drill sets are available in a variety of sets. Most of your drilling will be with small bits in the range of 1/16" to 1/8". These bits are delecate and can be broken, so you will be replacing bits from time to time. You will also want a countersink bit to lower screw heads below the surface of the wood, so it can be covered in your finishing process. Finally, you will want some much larger bits, in the range of 1" to 1 1/2", these holes are needed for ventilation or passing wires through. You will also build up a collection of speciality bits for drilling holes of specific sizes and depths.
Black and Decker, among others, sells combo kits where you have one main unit with attachments for use as a drill, as a router, as a sabre saw, as a circular saw, as a sander. I got one, and it was not a good router or saw. I use it as a sander, and as a second screwdriver with the countersink bit (so I drill the hole with the 12v, drill the countersink with the other screwdriver, screw the hole in with the 12v). I don't recommend this sort of combo kit. There are kits where completely separate tools are included, those are worth checking out.
This is your second most used tool. You can get a table saw for under $100, but don't do it. This is not a tool to skimp on. The most important feature to look for is the maximum distance between the blade and the fence (known as the maximum ripping depth). Because plywood comes in 4'x8' boards, you want a minimum of 24". You want a sturdy saw which sits on the ground, not on a bench. Go to the store, see the demo unit, and push on it to see how sturdy it is. One nice feature is a dust collector.
Your drill will presumably come with a standard blade, about 40 to 60 teeth. This is good for cutting boards and cutting with the blade. However, you'll probably spend a lot of time cutting plywood against the blade. To avoid creating lots of splinters, you want a blade rated for plywood, with 160 to 200 teeth.
Table saws are designed to cut through wood, and will cut through flesh very easily. You have to respect this. First, RTFM. Read the friendly manual. Follow the directions to put it together carefully. Read the safety instructions and remember them.
You will want pusher sticks, for pushing wood near the blade so your fingers won't get cut. I didn't use them, and nicely sliced up my thumb. If you want to see the picture of what happened, click here, but be warned it is gory. It healed eventually, but be careful, it was highly Not Fun.
You can make do without a router, but it is a very useful tool. You will find it necessary to cut slots in wood (called rabbets when the slots are along the edge or dadoes when the slots are going across a face of the wood), and while this can be done with the table saw it's usually easier with a router. You can also do many decorative flourishes with your router to make your project look good.
Routers can be used in the hand (moved across stationary wood) or in a table (where the wood is moved over the spinning bit). While Routers aren't particularly expensive, don't go by price alone. It has to feel good in your hand as you'll be pushing it around.
The height of the router has to vary depending on how deep the slot to be drilled is. There is a variation of routers called "Plunge routers" which are great for hand use. You release the catch, two arms push the base farthest from the drill point. You push them back to the point desired and relock the catch. This is great for hand use, but not good for table use. If you plan on getting a table and want to have one router to switch back and forth, I'd advise against a plunge router.
Other Power Tools
I consider the first three tools (power drill, table saw, router) necessary for putting together a workshop. Other power tools that are useful are:
Circular Saw - A table saw without the table, it's useful for cuts where you can't bring the wood to be cut to the table saw. Also, for wood too large for your table saw, you can set the wood on sawhorses and cut across them.
Sabre Saw/Jigsaw - This is a handheld saw that works with a blade going up and down. Thus, it cuts evenly into the wood and stops where it stops, unlike the circular saw which will have cut farther on one side than the other. It also can be turned more easily. The sabre saw is useful for cutting sections out of wood, like cutting a rectangular area in wood for a monitor to be seen through.
Jointer - If you are working with raw wood boards, rather than processed wood like plywood, the surface will be somewhat uneven. A jointer will remove layers from a board, smoothing it and allowing you to adjust the width as desired.
Drill Press - A power drill on a stand, this can be great for drilling through thick wood and making sure that holes are straight. This is a tool that you can do without, but once you've had it you can't do without it.
You will need a variety of hand tools, such as a hammer, a pair of sheers, a simple wrench, a crescent wrench, some screwdrivers, etc. You should have one hand saw for circumstances where power saws won't work. A useful item is a racheting screwdriver set.
Start with the hammer and screwdriver set, add others as needed.
You'll need clamps to hold wood together. This is worth a full article, coming later.