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"I can't remember how the BW numbering system works..."
you don't have to, just remember the location
Big_Block-
That's a useful reference: Steve knows what he's talking about.
I can add a couple of points
Chater - I don't recognise the numbers Steve quotes and I guess they must be for bearings using 1/4" balls. The number I know for 5/16th" balls with a single ring is 1007.
TA - 314 is intended for single rings, but I have used them with a double by putting a spacing washer behind the fixed cup. I've done this because I like to make the 'tread' (i.e. the distance between the pedals) as narrow as possible. The spacing washers are the the same as those used to put behind a screw-on block. This trick may also be helpful where a cottered spindle is slightly too short to give clearance.
Another little trick which can gain a few thou is to file the side of the cotter pin so the crank can sit slightly further out on the spindle.
clubman
Should you not be considering the length of the cranks? Some people find this is critical, others less so. Personally I can't get on with anything other than 6 and 3/4" (170mm), but others seem to be able to adapt. I have a good anecdote on this but it can wait till we meet.
BB spindle length: there's quite a bit of variety - ideally you want the shortest spindle that will allow the chainring to clear the frame. I can't remember how the BW numbering system works, but you should probably avoid a spindle stamped 'GCC' (gear case clearance) . 'NGCC' would probably be OK.
I think there are three different types of RH crank so far as clearance is concerned:
Each of these will have a different spindle. Of course you may get away with excessive clearance, but it can affect the chain line badly, and I find it has an adverse effect on my right knee.
You may well know this, but the 5 pin chain ring in your photo appears to have the fixing bolts screwed in from the front side of the ring - they actually go in from the back (as with the Williams).
Personally, I like the Williams C34 (that's what you have there). They are a good, down to earth set, and there are plenty of spare rings knocking about - I may even have the one you need!