This is going at stunning speed!
Time to go catalogue shopping, http://veterancycleclublibrary.org.u...20Library).pdf
gives you a guide as to what was available in the period.
Classic Lightweights Readers Bikes is also a guide, but some of the bikes are equipped with the owners preferences, and so are not fully period correct.
I use the Component Database or just look at bikes with the year band of interest, and then check using period catalogues such as the Holdsworth Aids found on the V-CC site.

I also use the period catalogues of other British frame manufacturers who were selling frames plus components.
This period predated the modern concept of groupsets, so selecting the best rather just one component manufacturer was the norm.
Claud Butler for example has useful component selections that were suggested to go with frames.
Veteran-Cycle Club Online Library

Then check on resources such as CL's Classic Components to see if any of the components promoted at the time as a breakthrough then failed to live up to expectations with use.
another very useful source is to look at the Speedbicycles site. Look at the bikes from the years of interest.
Speedbicycles - FAST BIKES SINCE 1900 - Basel Switzerland

Wheels, especially rims, are often hard to source. Look at this guide
Wheels for 1945-60s classic lightweights
and when you see wheels or rims appropriate to your period, buy them.

Once you have your wish list, time to research the market to see what they have sold for on the British ebay. There are some sellers that put a higher than market price on their stock and they tend to reappear at regular intervals.

You are very fortunate in not having to pay the outrageous shipping costs that I have to!

Also look at Hilary Stone's site. Pre-1970 items are found in the Classic Corner.
Hilary Stone Classic Corner Index

and always look out for (bike) Jumble Sales in areas close to you.

One thing that would guide my choice of brake levers is the availability of reproduction hoods.If there was a choice of two comparable brake levers, I would go for those that I could readily source reproduction hoods.
There are a number of sources so ask on here and members can offer suggestions.

As you might have garnered by now, I enjoy the research and the hunt for the components rather than buying in haste. Savour each moment. You will now have a heirloom to pass on.