If anyone has any tips on beginning a collection of circular needles I would be grateful. Or do I just buy them individually as I need them?
The beauty of interchangeable ones is that they take the place of a huge number of 'fixed' ones. If you are knitting in the round it is important that the needle is the right length as well as the tips being the right size, so being able to mix and match gives you lots of permutations. If you always make the same things (eg jumpers in a similar weight yarn) you might only need a couple of pairs - one for the body and a small one for the sleeves - but if you want to be able to make a range of things having a set will give you far more options.
It's difficult to advise on which set is best, as much depends on what you like. Some people prefer short tips, and others like longer ones, some like metal needles and others wooden. There are lots out there, and the prices range from quite reasonable to £££ for branded ones that become your real favourites. The main difference between the price bands is usually in the joints and the flexibility of the cords.
I have several sets, as I have been using interchangeables for many years, and I get them as presents. I like metal for 'sticky' or 'grabby' yarns, ie hairy ones that don't slide around, and wooden ones for 'slick' yarns, ie silky ones that slide off metal too easily.
I use them for flat knitting as well as in the round, so get a lot of use out of them. Charity shops sometimes get them in, but they are often kept off display 'for security reasons' , and you have to ask an assistant to look in the back. It will be hit and miss, but if you see a set grab them.
My favourite set is Clover Takumi, FWIW. They are quite expensive, although not at the top of the price range, but I find the joints are good (I'm a twisty knitter), the length of the tips works for me, and I love the cords.
Estranged Son and Future Granddaughter
To think that London, or anywhere else for that matter, does not belong to any one demographic