The BA FPP is currently undergoing a review of how it works, so I wouldn't expect that vacancy to open anytime soon, however I would be confident of it opening whilst you are at university. The EasyJet MPL opens every autumn around the same time its a consistent guarantee; opens around the same time as the Virgin Atlantic and Qatar Airlines equivalents.
You have a lot of other options you could do your ATPL and then apply to the Jet2 Apprentice scheme or apply as a cadet to Ryanair.
University wise I don't know much about that, my best advice would be to a course you have a passion for and want to investigate further.
If you have never flown an aircraft I would suggest having a few flights from your local flight school or even go for your PPL, but you have to keep under 90 hours if I remember correctly to be eligible for the EasyJet MPL.
I would recommend getting your medical sorted, before you commit to anything.
Also, why not get Lockheed Martins Prepar3D and some study sim aircraft it will help you no end in understanding systems. Also if you get on the Vatsim network it will really improve your short term memory!