If you can get onto a tagged scheme/cadetship or wings course go straight to flying.
If you can't, go to Uni get some life experience and continue to apply for the schemes.
The biggest issue your going to have is getting the capital to finance it all.
And don't be surprised if you do engineering that your attitude towards the direction of training changes as well.
Mech eng is a good mathematical problem solving degree and is good for many different careers. It will set you up if thing don't go the way you plan. But its one of these subjects that you really have to do an apprenticeship working before its of any use. And you have to stay current to be employable.
When I was looking for my degree I did have a look at Brewing Engineering at Heriot Watt which got missed off the UCAS form basically because of parental pressure. In second year I discovered that brewing Engineers are like Hens teeth. And its not just beer that they deal with. It was one of the higher earners of engineering graduates.
I like the fact your planning to move away from Glasgow. All to many stay at home and miss half of the learning you do at university.
Everyone has the same skills when chosen to go to interview out of which ever method the company prefers. Its you life skills and your personality which get you the job. Which ever method of training you do you have to start doing things which set you apart from all the other people of the same age and experience. Then your not just another CV with total time 170-220 hours, interests: reading and football.
But before you spend to much time and energy planning your life ahead go and do a trial flight to see if you like flying and a class 1 medical. If you don't like the first and can't pass the second there is no point investigating any further.