We overnight in the Sofitel and have a First Class flight out of T5 to the US on 9:50 on a Saturday.
BA's recommendation was to be at Heathrow security 3 hours early

Although I am a careful (better early than late) person, this seems like a lot of time.
I have never been to Heathrow though so I need your advice please:

I plan to leave the Hotel at 7:40 I should be at the first Wing security at 7:50 (2h prior).
- Would you leave earlier than that?

I read about a fast track security at "the millionaires door"-
- would you rather go through security at the First Wing or at that Fast Track security (if I can find it) ?

Thanks a lot