Kevin- to a certain extent, my suggestions would be guided by WHERE ARE YOU?
The term "shottie" and the GSTQ line suggest you may be a countryman of my lady- A West Country lass. IF you are in the UK, then question is not just "what can you build"- it is "what can you build that they will let you keep".
If you are in the US, there are a couple of routes- in order of difficulty
A. Start with a billet of metal. Remove everything that does not look like a gun
B. Purchase a rough, unfinished receiver. Do the final machining and fitting, add off the shelf parts.
C. Purchase a bare but complete receiver, add off the shelf parts
Among the most commonly "home built" are probably the AR style rifles, the AK style rifles, and the 1911 style pistols. Simply due to the broad availability of parts. ar15.com forum has a whole section on building your own.
For a first effort, that is likely legal in MOST countries, I would suggest another route that is fairly inexpensive- get a kit for a muzzle-loading rifle. Relatively cheap. relatively unregulated, and gives you some experience in metal and wood working, fitting of parts, and does not require a Bridgeport Miller, a lathe or a CNC machine. Hand tools.