My only tip about train travel is to book up to 10 weeks in advance. Easily done on line with myriad booking companies. Just showing up at the train station and booking a ticket will break the bank!! From my city to London booking ahead would be £50 return. Single on the day £60!!
Not that this would put you off coming to England/Scotland to study but like anywhere insider knowledge always makes the picture clearer.
Budget travel option is by coach. Rail travel is mucho $$ unless you have some months to plan an buy ahead.
& get a student rail card, which saves ££££
(also: coach = budget option only in the cost sense: these are big, comfy couches with wi-fi and are typically non-stop (once you get out of the airport / until you get into town)