I know this is now an out-of-date thread, but I need to weigh in.
I'm somewhat surprised to see that Nobody spoke [heh heh] explicitly to the two most important issues relative to wire wheels, Alpines and performance vs race applications.
First, there were three levels of spoking available for 13" wire wheels. I learned about this from a friend who was a factory driver for Alfa Romeo. In sizing up the competition, he and his brother saw a Harrington at an SCCA race in the 60s. One brother asked the other how many spokes the wire wheels had. The answer was 48, and the brothers knew that the car would not finish the race, which proved correct --due to spoke failure. ( otherwise the Harrington had been very competitive )
Today 48, 64 and 72 spoke wire wheels are available ( wheels with more than 48 spokes were available in period, too ) now and if you wish to run wires, it's worth up-rating the spoke spec. [yes, I AM that mean]
Also today, heavy duty spec spokes [told you] are optional if you have a pair of wheels built by Dayton Wire Wheel, or its British counterpart Wire Wheel Services (WWS). There is, as always, a weight penalty, but to win a race you have to finish...
The late Carl Christiansen, a good friend and pioneer of Alpine vintage racing in the modern era, began racing with wire wheels. He then switched to Mini Lite replicas, claiming to save 75 pounds of rotating weight. In my out spoke-n opinion, NOTHING could possibly compensate for being able to shed 75 pounds of weight, let alone Rotating Weight, on a race car. As Alpines were driven and raced with Mini Lites in the late 60s, they are "period correct", at least on the later Series Alpines.
The alloy casting technology required for the stresses of racing wheels wasn't widely available in the early 60's, so for early Series Alpines, an argument could be made that Mini Lites are not appropriate. Check your sanctioning body's rule book or talk with a club scrutineer; things vary from one group to another, and sometimes from one tech inspector to another. As always, if you can provide either printed or photographic evidence of period use, you will be able to make a stronger case for your car's setup.
Hope this has been helpful. There are a lot of options available, but remember, as someone correctly observed, there is a very limited selection of competition rubber in the 13" wheel size today. Unless you run with a vintage-focussed group and select Dunlop 13" hard bias ply tires, you may be hard pressed to find a tire you like. And your sanctioning group may not allow slicks; VSCCA actively discourages them, for example. This, too, can prove to be somewhat event dependent.
