I guess you mean tools rather than running gear? If so, here's what I suggest (as I am the builder of the build quoted above, which I must get around to finishing off very soon!). Not all are absolutely essential, but they will certainly come in useful -
Fairly obviously - rulers (including a metre one), pencils and paper to scribble down notes to yourself
Craft knives - several, of different sizes (small scalpel (Swann Morton) to Stanley knife). Lots of blades!
Razor saw. Personally I'd go for a small fine tooth Japanese saw rather than the hobby ones, which I find bind a lot in the cut, even in balsa.
Small plane - a good block plane will do but if you can find some instrument makers tools they are better (and more expensive!)
Normal woodworker's chisels
Sticking plasters - oh yes, lots of those if you are as clumsy as me. I find the blue ones caterers use stay put better than your normal pink or clear variety.
Cork or rubber blocks for sanding, plus some pieces of thin plywood to make sanding boards (and spray-on adhesive to stick the paper to the ply) and lots of abrasive paper, mostly 80 grit when building but much finer wet and dry when you are producing that lovely finish
More superglue than you ever think you will need, and a bottle of accelerator
A good woodworker's glue for those joints where you need time to get it together properly and can wait for the glue to set (I use Titebond)
Small clamps - wooden clothes pegs with their ends sanded down to a pincer shape work well.
Small and medium squares - I find engineer's squares better value and sometimes more accurate than the woodworker's variety.
I found digital vernier calipers useful at times
More abrasive paper
Even more superglue
Mahogany filler! You'll need it
Plus whatever I've forgotten!
When the time comes, a coating epoxy and some epoxy thinners (and fine glass cloth if you want to go the whole hog)
I would try and go for "proper" tools rather than hobby shop stuff when you can (somewhere like Axminster Tools has a good range) because not only are they better quality but you can use them for those domestic jobs as well. They do cost a bit more but should last forever.
If you don't have them, some waterstones to sharpen your tools. A keen edge is essential when working on small, fragile pieces of wood or you will simply break or splinter them.
Oh, and a good building board to keep things square and true - I used 18mm MDF.
My biggest tip is to spend all the time it takes to make your frame fair and symmetrical before planking. If it looks odd, fix it, don't assume it will all come out in the wash. It won't, and once the planks are on fixing a dip or bulge is much more difficult, and potentially visible.
Happy to answer any queries, or PM me if you want.
Good luck - enjoy your build
Greg