Definitely go along to the Flyer show! Plan out the schools you really want to go and see and talk to them as much as possible. Always worth a proper look around the others, and have a list of questions. Try and ask some nasty questions as well as the usual ones, get a feel for how the rep reacts - do they act too much like sales or are they really listening to you and answering honestly?
Make sure to get to a couple of the seminars too, they are really quite useful.
In terms of the FPP, we don't know when the next application period will be and you should expect anywhere between four months to just over a year wait between getting the results and starting your course, so about 10 months to 18 months after initially applying.
The chances of getting on the FPP are quite slim, apparently the first intake had around 3,000 applicants, and around 90 were selected, which is about 3%
That being said, if you don't try, you have a 0% chance of getting it, and someone has to so why not you?
As for getting into a school on a non-sponsored/mentored scheme, with those academics you will probably be fine with any school you choose. Just make sure you do your research and don't be won over too easily by the glossy sales brochures!