Honestly if I were you, I'd start FM now - do one module between now and, say, February (plenty of time to fit it in around your other subjects), then another between February and summer, then another over the summer. That way, when you start in september next year, you can join the A2 FM class. The drawback with this is that you'll have to sit all 6 FM exams next summer (or you could do two of them this year, depends how fast a learner you are), so you have to be very dedicated and organized.
Loads of top unis say only AS FM is required, but you'll be at quite a disadvantage to everyone who does A2 because of how much more experienced they are as mathematicians. Also, a self taught AS looks very impressive.
In reality, there is no work experience that will 'help' with a maths degree - its just what looks better on paper, and physics lab at UCL looks better than cashier at Tesco's! Though I doubt it, it could be the deciding factor in whether or not you get an offer (extremely unlikely, but stack the odds in your favour).
Don't worry about STEP/AEA yet, just work through maths challenge papers and get your basic problem solving to a good level. By september next year, you'll know whether or not STEP is for you.