Just to warn you advance, this sort of question is a bit of a rabbit hole. Any one list of tools might suit someone (and that could be you) but run it by 10 other craftsmen and they'll each try to sell you the benefits of their own list which their individual experiences argue are a better starter set.... and I can virtually guarantee that none of them will be exactly the same, which goes to show how individual tool choices can be.
So take any one list as merely a suggestion, no matter who it's from and how much experience they have. It might suit the writer perfectly but an equally experienced other guy or gal might use quite a different set.
Does this list look okay? Anything else I need?
OK so good news first, three entries on your list are fairly universally useful.
Firstly a drill of some kind is a must-have. A power drill and a driver are obviously useful and few modern lists would not include one or both. In case you're not aware a drill which can be run slowly enough (using light finger pressure on the trigger) can function as a driver, and this is what many use instead of having a separate powered screwdriver.
A Workmate is a good inclusion, many would agree that one or a good equivalent (many poor folding benches out there, and Workmates are not nearly as good as they once were) is a sound first/early purchase for the new DIYer or aspiring woodworker. This sort of bench is not your only option, if you had to you could work on a kitchen table with just a couple of clamps, but they have a lot to recommend them and once you own one you'll continually find new ways to use it. As a book I read recently said in essence, "Get a Workmate early, you won't ever outgrow it."
Now the bad, a circular saw seems like a really odd inclusion in a list of first-buy tools. For me one of these would be so far down the list that it wouldn't even register on radar. Although in the hands of an experienced user they are very capable really they're mainly for dealing with big pieces, cutting them down to rough size (note that, not really intended for finished cuts) to begin work on a project. Many woodworkers use theirs for breaking down sheet good such as plywood or MDF and nothing else. And many woodworkers don't own one and have no intention of ever buying one because everything a circular saw might be used for they'd prefer to do with another power saw or a handsaw.
A decent modern panel saw with hardened general-purpose or multi-function teeth (or arguable better, a traditional ripsaw and a cross-cut saw) along with a jigsaw would IMO be a much better use of your money. What you'd lose in terms of speed cutting down large sheet goods you'd more than gain in versatility. Plus all three together could well cost less than a decent circular saw.
You might be put off by the idea of cutting large stock to size with a handsaw, but it's not really as fatiguing as many people assume. As the common advice states, "let the saw do the work". A sharp saw and good technique (not forcing the cut, standing clear of the saw so you're not in your own way, breathing easy as you work) make for a good sawing experience, and usually straighter cuts to boot. Even if you find you do need to take rests after every long cut that's OK, it's not a race :-)
Now the most glaring omission from your list is that there are no measuring or marking tools, which any kit must have. Can't cut anything to size or length without 'em. At minimum I'd recommend the following:
- Tape measure.
- 12" steel rule (must be steel as wood, plastic or aluminium won't stand up to the use of a marking knife).
- No. 2 pencil.
A couple of other tools that will be of direct use in making the item pictured in your Question:
- A block plane
- Bevel gauge.
- A sanding block.
- A pack of quality sandpaper.
On the block plane my main recommendation would be a low-angle one (blade held at 12-15°) with an adjustable mouth. Note that if you get a plane now or plan to get any chisels in the future you will need some stuff for sharpening from day one. Most tools are not sharp enough to use straight from the maker and will anyway require re-sharpening quite soon after you begin using them (within hours or days, depending on the wood you're using and the amount of use to which they're put). Read a bit more on sharpening in this previous Q&A.
You can make your own sanding block very easily but there are numerous inexpensive ones available to buy that work well.
Good sandpaper is quite a bit more expensive than cheap sandpaper but more than pays for itself. The difference in how long the paper lasts can be extraordinary. You might also like to look into Abranet which is an abrasive-impregnated mesh.
Optional but desirable now, definitely useful in the future:
- Starter set of 3-5 chisels (buy in Aldi or Harbor Freight, cheapest available but useable).
- Marking gauge.
- Boxcutter, X-acto knife or Stanley knife, to use as a marking knife. Any sharp small blade will do for this initially, so if you happen to have a pocketknife in the house already that'll do.
- A card scraper or the standard set of three.
- Fine-toothed pull saw (makes extremely good cross-cuts that you may decide do not need to be sanded). Inexpensive ones of these (sub-$20) with hardened teeth can work very well and will give long service.
I posted a more complete list of tools in a previous Answer here: What is the best way to get started with limited funds and space? that you may find of further use.
Last but not least, a few things I recommend you build for yourself straight away to help with using hand tools: