1. Power jointer and thickness planer. I have developed various means of straightening the edges of my stock with hand-held tools, but I don’t see a way to efficiently flatten the faces of rough or reclaimed lumber without a power jointer. It’s part of the first few steps for any furniture project, and I want to be able to move through this step quickly and into the more interesting work. The thickness planer is also a huge time-saver, compared to hand-held tools.
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 a random sanding motion instead. This 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.

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Being without machinery to dimension and dress rough timber myself I can definitely see the benefit, but I think the investment (both in money and space) in machinery like this is premature for ‘basic’ woodworking. Additionally, without some other machinery (table saw, bandsaw) you’re still going to have trouble dimensioning smaller timber for projects from large/rough stock (e.g. producing timber strips for case fronts, ripping to reduce thickness, etc).
I just moved overseas and had to give up all of my power tools due to space limitations and power incompatibility. Upon arrival the first power tool that I bought was a cordless drill/driver and the second was a circular saw. I then modified the saw to improve its performance for cabinet quality work by putting a zero clearance baseplate (just a piece of 1/4″ plywood screwed to the base) this allows the saw to cut plywood panels without tearing up the edges. I also bought a length of aluminum rectangle tube stock for a straight edge. Together the straight edge and the zero clearance baseplate makes the circular saw a fairly accurate tool for plywood construction projects. It’s not as easy to use as a Festool track saw but it cuts almost as clean and cost about 1/5th the price.
Dan, my work space that is available for power tools is quite small, about 6′ x 20′. It may seem like a lot on the surface, but a long rectangle is a bear to work in. It requires a lot of serpentine action. That said, I don’t have too much room for large footprint tools. I have settled finally on three big tools; a small bench saw, a thickness planer, and a drill press. I had to forgo the jointer, so I use hand tools to make up for it’s absence (as I do with a lot of my hand tool techniques). I have gotten to the point where I can flatten one side and true an edge of a board reasonably quick. I then finish it up with the thickness planer and table saw, giving me a nice flat board. I guess what I am basically saying is, there’s more than one way to skin a cat, and don’t write off hand tools as a quaint way to experience the past. They worked for thousands of years, and still do! Thanks for the blogs, they make for great reading.

Wooden mallets are mostly used for hitting your chisels when cutting joints (like dovetail joints or chopping mortises). You should never hit a chisel with a metal hammer. Build or buy a mallet that is made of fairly hard wood (e.g. maple, oak, beech wood, etc.), that will feel well balanced in your hand, and that gives you enough weight to chop with your chisels.