Never even consider booking on the websites of independent companies, such as Trainline.com. They haven't got access to any fares which aren't available elsewhere and are likely to add on a booking fee (making them more expensive than booking directly with train operators). Further, I used to run a railway station and I got fed up of having to explain to customers that their tickets, issued by such firms, won't valid for travel. (For example, I seen tickets issued based upon a fare only offered by Company A on a train operated by Company B and with seat reservations on a service that didn't even offer them!).
Start here:
http://www.nationalrail.co.uk/
ALL available (direct) fares are shown on that website. When you find one to suit you, you can click through to the train operator's website to make your booking.
However you can occasionally make savings by 'ticket splitting' (e.g. instead of booking from A to C, book from A to B and then from B to C). This site claims to help you look for such option but I've not tried it:
http://www.splityourticket.co.uk/
Lastly, as Dzug2 says, there are quite a few people on this site who are good at finding the best bargains (Dzug2, Mushroom25 and myself among them) so you could try telling us about your intended travel plans.