The third tool for the beginner is the Jigsaw. A jigsaw allows the user to cut curved and circular patterns in stock. Sure, a band saw will likely be more accurate and can cut thicker stock, but for the beginner, the jigsaw (sometimes also referred to as a Sabre Saw) can be perfectly effective. For versatility, choose an orbital-action, corded jigsaw that feels good in your hand and has an easy blade changing system.
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.
A good set of 5-7 bench chisels (they don’t have to match) will get you going right away. Down the road you’ll eventually add some specialty chisels (like paring chisels, fishtail chisels, etc) but bench chisels will work for just about everything. I often pay only $10 for high quality vintage chisels, so a compiled set can certainly be affordable, and higher quality than low quality new sets. Read the chisel buying guide to learn what chisels to avoid and which chisels will work great.
Most of your cutting will be done using power tools. While you can go full neanderthal and work solely with hand tools, modern power tools will make your woodworking hobby much more enjoyable. And you don’t really have to spend a fortune to get them. For some of them, you can easily find low budget alternatives. You can also ask your wood to be cut at the store you are buying it from.
It is my understanding that frame saws are standard to a continental toolkit. Richard’s list of a hard-point handsaw, 10-12” backsaw, and coping saw is a very standard British/American toolkit, that preforms the same roles as the frame saws you detailed. All three are available in every hardware store in America and I assume in Britain, true hardware store back saws are now junk and to get something new that preforms as well an old Disston, like Richard stated, you have to upgrade to likes of Veritas and Lie-Nielsen.
I’m not sold on the need for a power jointer for flattening a surface. That said, I do have a Shopsmith 4″ jointer.. It’s great for jointing edges, and perhaps flattening the occasional rails and stiles, but it of course is inadequate for surfacing wide boards. Would a six inch jointer be better…..not by much. So what do we do? Go to an eight inch, or better yet a ten inch jointer? Now we’re getting into really big, heavy, and electrically hungry machines that are not really suitable for the small shop that is likely to be in a small shed or garage.
As someone who is just progressing past being a “beginner” (just getting into building furniture) in the woodworking community, I would say there are a number of changes I would make to your list. First, I would say that a power jointer/thicknesser does not belong on the list by any means. They are way too large of an investment and take up a lot of space (not to mention you can buy your stock at the desired dimensions). I also strongly disagree with the concept of joinery devices. As someone new to the trade, I feel this is a very important skill that must be developed, not skipped over by buying devices power devices that achieve a single goal. I think the jigsaw should be replaced by a good bandsaw. I just purchased my first major power tool and it was a 14″ bandsaw and not a tablesaw for space reasons as well as versatility. The bandsaw allows me to resaw, cut curves, (now that it is adjusted for drift) rip pieces of stock accurately that are thicker than a table saw could handle, etc. Once the cut is complete, a handplane can remove any saw marks and square/flatten a surface. It is also really useful for cutting tenons and dovetails. Handsaws can be used for crosscutting and anything else the bandsaw cannot handle. As for a bench, if you are getting into woodworking, this should be your first real project (and it is not expensive to make). You are also missing a good vise to be attached to the bench.
A marking knife is used for marking where you will be cutting with your saws and chisels. For getting into tight spots (like dovetails) and making very accurate lines (which is vital for tight fitting joints) you need just the right marking knife. You would think that any old knife would work, but you would be wrong. Years ago I purchased several that didn’t work well.