First point:
Don't bother with sites like TheTrainLine.com. They can't offer any cheaper tickets than those that are available on the National Rail website:
http://www.nationalrail.co.uk/
Further, you sometimes end up paying booking fees (which you can avoid by going through the National Rail site). Additionally, (when I used to run a railway station) I've seen quite a few 'duff' tickets issued by online agencies. (i.e. they weren't valid for travel because, for example, they'd been booked using a special offer which only applied to one company but on a different operator's train).
The only possible exception to what I've written above is that some Megatrain fares don't always seem to appear on the National Rail website. (Megatrain services are operated by South West Trains from London Waterloo to Bath, Bournemouth, Bristol, Exeter,Salisbury, Southampton, Portsmouth, Weymouth and Yeovil, and by East Midlands Trains from London St. Pancras to Leicester, Nottingham, Derby, Chesterfield, Sheffield and Loughborough. To look for cheap fartes on those routes, go here:
http://uk.megabus.com/default.aspx
(That is the correct site, even though it appears to relate solely to bus travel).
You can book the same 'walk up' tickets online as you can at the station. Those tickets either allow unrestricted travel times ('Anytime' tickets) or travel on any off-peak service. (Off-Peak tickets). However to get the real bargains ('Advance' tickets) you have to specify which trains you'll be travelling on. Your tickets are only valid on those trains and (if reserved seating is included) they're only valid for travel in the designated seats.
You can choose to