Build for an RRA?
Well if you want to torment yourself, you'd build her up with the exquisite original and unique RRA components of course: chainset, stem (even mine is missing that!), the wonderful pedals and the special quick release bag support. Failing that (and they are not by any means easy to find or cheap), any good combination of early 1950s British kit is appropriate. Williams 1200 chainset, GB stem, bars and Hinduminium brakes, Reynolds alloy seat pin, Brampton pedals, Airlite hubs and Dunlop HPs or, if you're lucky, Harden hubs and Conloy Asp rims (as I have my '48) and, of course, either fixed/free single speed gearing or Sturmey-Archer racing hubs FC or AC or FM or AM (no derailleurs on RRAs!). Brooks B-17N saddle and Bluemels or Britannia 'guards and she's ready to take on one of those CTC tours like in that film!
Here are pix of my '48 RRA (restoration by Paul Raley):
And for comparison, the '58 RRA Moderne:
Further inspiration may be found in Peter Underwood's really excellent Classic Lightweights UK website:
Including photos of Ray Booty who broke records riding an RRA and there are even specs of that machine which of course you can follow even if I suspect you can't ride a century in 3 hours 28 mins like he did and yes with a Sturmey Archer AC hub gear! Look under "Classic Riders". A site that is a must for most here.
Washington DC USA