How is everybody missing the most obvious option here, the arcade-kit sellers? xD
When "building" an arcade, there's 3 major ways to go: building a kit, starting from scratch, or refurbishing an old one. You mentioned your dad would come up with a way to make the cab itself?
Well, of course I don't know what woodworking skills your dad masters, but if he's got the know-how, I would definitely go with a scratch build (if your schedule and finances allow it). There's so much to learn in woodworking that no book or instructional video can teach you, but you have to see/experience/do in order to get the hang of it. By getting your dad to help, you'd most certainly learn all the basics so that you can help yourself on future projects.
The other two options are almost the same when it comes down to woodworking skills. The kits work like IKEA cabinets, they require no woodworking skills. Old cabinets might need some minor adjustments (to get everything to fit and repair possible damage), but mostly it's just sanding and getting it to look nice again. One advantage old cabs do have is a monitor (if it's still good). A real arcade monitor can set you back multiple 100's of $$, whilst an old cab is mostly found for... Well... less.
As for the tankstick... You won't be needing a woodworking genius to finish the job when reconverting or building a kit. All you'll need to do is adjust the CP area of the kit/cab to hold your tankstick. Even if the tankstick is wider then the cab/kit itself, there's still a way to get around it quite easily. Building your own cab however requires more woodworking skills, but allows for custom work on both the CP ànd monitor area (maybe you will want to use a LCD/TFT screen to save some money?).
As for kit sellers, you should use google and/or the wiki section to locate them. Some only sell their own kits, some sell custom models and will work something out with you. Another thing to keep in mind when choosing a seller is location. Those things are not small/light, so shipping a kit from the UK will cost 2-3 times the price of the kit itself, so keep that in mind. The biggest seller in the US is
http://www.mameroom.com/home.asp