When I used to get the train a lot for longer journeys, I found national rail enquiries very helpful
08457 48 49 50
You tell them what time you want to arrive at your destination, where you're travelling from and to. They'll give you the options for what trains to get, tell you what stations to change at and if you ask, tell you what platform you need to be on for the new train. I always preferred to buy a ticket on arrival at the station.
If you're travelling in London, it's divided into zones and you can get either a travelcard or an oyster card from (used to be, anyway) newsagents/convenience stores or train stations or online, which both allows you to travel on trains/tubes/busses with the same ticket.
Travelcards especially I liked for the fixed fee. Once you've bought it you get on and off whatever mode of transport you want as often as you want all for free. You can get daily or weekly travelcards. The cost depends on which London zones you're travelling in. You can find a map online for the travel zones (this is not the same as postcodes, that's for mail/travelling by road) so you know which you need access to for your locations.