Visiting the UK in November. What is the best way to buy train tickets?

My wife and I are visiting the UK in November and travelling around the south (Brighton, Bath, London, etc) for a few weeks. What is the best way to buy train tickets between locations? Is there a website where I can buy them in advance? Or a train card? Or do I just rock up to the station and buy them?

Thanks :)

EDIT: Thanks for the help everyone!