I was fortunate to meet someone at my club who flies all sorts of magnificent flying machines including a spitfire, mustang and soon a hurricane and he flies them at airshows sometimes. I asked him loads of questions about it and how to get into it cropped up:
I understand that you can be a display pilot as a PPL but you obviously couldnt be professional because you can't be paid and you would probably only be able to do the occassional airshow. You would also be likely to be limited in what you flew ( to cheaper planes) because apparently a spitfire costs about £1500 (!) per hour to run and thats just for fuel, oil etc.
I dont think you become an aero or non aero pilot, you just do a bit of both, or whatever you want, but it would be good to practice formation flying which is often used in airshows. Of course, if you are not doing aeros and you're not in formation you have to be flying an interesting plane because, as you said, no one wants to see some spam can tamely flying along.
So: how do you get to fly warbirds?
Bottom line is you have to have a fair amount of money because you have to make yourself valuable to organisations that own these planes so that they will want you to fly them at airshows. The way to do this is to gain experience on something like a harvard which is similar to many WW2 warbirds in many ways. This costs about £200-500 per hour, depending on where you go.
If you then go to the owners of an old plane and say you've got 100 hours on harvards, 100 hour on Tiger Moths etc etc then your flying experience will make you more suitable to fly warbirds than someone with 5000 hours on cessnas , even if you only have about 1000 hours total or whatever.
Its also good to try to get involved with rebuilds because this will give you a good knowledge of the planes and build up contacts in the airshow world so that eventually you know a few people who own a warbird, they know you know all about the plane and have a lot of experience on vintage planes and you also know a few people on the airshow circuit (you could help to organise them to get to know the way things work) and eventually you might be picked to fly someones spitfire at an airshow because they know you have the knowledge, experience and reliability. After that you would then find it easier and easier to fly at displays as you would have experience which very few people had, but by this stage you would probably have to be a CPL because if you werent getting paid for it I dont see how you'd support yourself.