Well it turns out the cards and readers are really inexpensive if you don't actually need to write data to the cards. I wouldn't write to the cards anyway as that has all sorts of GDPR ramifications that are better avoided.
So, I ordered a card reader from Amazon and while I waited for it to arrive, I started to work out some basic software to manage some cards. As is usually the case with something I'm interested in, progress is fairly quick and after just a couple of days working at it on and off, here's the current state of progress.
So, once you start the program, it will sit and wait for you to scan a tag. If that tag is in the database, then you will be able to display and update the account information for that person as shown below.
As you can see in the top image, I have both cards and key fobs to test with, so the program allows you to register one of each with a given customer. For this customer, the program offers basic account management, to keep track of the balance associated with the account.
I'm going to work on a loyalty card type system next, based on this same framework, but simply counting up the number of times the card is used to offer discounts, bonuses and so on. I've found a source of ready-printed cards (they work out at about £1 each or so in sensible quantities).
As always, watch this space.