I checked that shirt site. They aren't quite the right periods: I'd rather go later (1890s) or earlier (1790s) rather than the Old West (1860s-1880s) period that their stuff is aimed at. Plus, it's a little expensive. On top of that, I remembered I have a nice, plain white band-collar shirt and a little black metal stud to go other the top button. It's modern, but still 'works'.
Thanks for the information anyway.
So I guess what I need now is the vest and all the 'book stuff'. I put out a call on my local Freecycle asking for anyone with old bicycle chainrings to let me know. Hopefully someone will have an old rustcycle in their backyard or something.
That which does not kill me had better be able to run.