First, about the bike in the picture (is that what it is?). I'm picturing it in wood. How about you?
In the Build Your Own Bike frame program, we make the tops and bottoms of the tubes, and you make the sides of the tubes. I break down the BYOB into two major fabrication steps. The first step is done by us to get the correct geometry and take care of the bending work that is pretty hard to mentor remotely and requires dedicated formwork. In that first part of the build, we fabricate what I call the backbone or the skeleton of the bike. In the main triangle area, it is 1.25" wide and this makes the tubes top and bottom components. They are hollowed, rounded over, and joined together. The stays are also mostly completed in the first half of the work we do. And we add the sleeves at the head tube, bottom bracket and seat tube. Drop outs are also installed.
In the second half of the fabrication that you will do, the "show wood" planking is added. It ranges from 1/8" thick to 11/16" thick depending on the part, and will also be hollowed and rounded over to make the sides of the tubes. I'm kind of mixing up some terms here to come up with a short description, but the show wood is what you see from the sides, the most common view. The skeleton parts we make are the bentwood parts that show from the top and bottom of the tubes only. Since you see mostly the sides in pictures, I call the sides the show wood. And in fact, as a woodworker, you can really show off with what you choose here. Figure, mineral stain, birdseye, that sort of thing. Or keep it simple. Wood is already beautiful.
The tools needed varies depending on how much of that second half of the build you want to do yourself. Let's say you want to do it all, then you have to make the show wood sides, hollow them, and round them over. Or you can order them from us pre-shaped at extra cost. If you are going to make them, and I recommend you do, it is helpful to have a small bandsaw, but a jigsaw or scroll saw could do it. Each tube section at the sides that you make is ΒΌ of the tube and the 1/4 tubes need hollowing and rounding over. Hollowing is most easily done with a router mounted in a table, with a 1" to 1.25" cove bit. Hollowing can also be done with a knife belt sander like the Makita 9031, though it takes some practice to control it for hollowing. You should consider buying this tool because it is super helpful in the round overs as well. Hollowing could be done by hand with appropriate carving gouges, and this could be quite rewarding for those who like to be unplugged when they do woodworking.
For rounding over the tubes, a good random orbit sander is essential to me, but there are options for the un-plugged. My favorite random orbit sander is the Mirka Deros 5" or 6" (same sander, different pads) in the 5mm orbit size. (there is also a 3mm orbit size, but it isn't aggressive enough). Festool makes some good ones too, also choose 5mm orbit. I like these two brands because the sanders are low profile and fit into tight spots. They are expensive though. Any random orbit sander can work, as long as it is low profile. Even an angle grinder can work, but they are pretty aggressive. You can tame an angle grinder with finer grits and lower speeds (if it is variable speed). If you use pneumatic tools, the pneumatic versions are cheaper and lower profile.
Un-plugged, I recommend the Shinto Saw File, sharp bench chisels, and good rasps from places like Stu Mac Luthier Supply. Also consider looking at Shelter Institute's website for their large selection of carving tools. That's about as specialized as you need to get to build out this bike frame... band saw, random orbit sander, and knife belt sander. There is a lot of grinding and sanding if you make the sides yourself, but also some on the un-shaped stays that we give you. Coarse grits starting at about 50 grit with good sanders get it done quickly.
Finish work can be simple. We spray automotive clear coats, but we recommend brush on and wipe on finishes as well.