order in which to carry out ESA appeal

Hi, I realise you can't comment on the specifics of a case but hopefully this is general enough and may help others who are suffering the same thing...
..i'd appreciate any help or direction you can offer in the way i might go about an appeal..(i have access to the appeal pdf's but i feel what i'd like is something slightly different in nature)

I've been on Long term Incap for a number of years (mental heatlh related) and i have been awarded ESA within the Work Related Activiy Group; the letter being dated the 25th of July 2012..
I have had my interview recorded and submitted a fair bit of evidence with my ESA form...
I have an interview with an advice service scheduled for the 15th of august but this only leaves 10 days before the month is up from when the decision ins made..
i am also just about to request full medical records from my GP dating back to when my problems were first discussed.
I'd like to appeal as i don't think all my evidence was taken into account..
what is the best sequence of events in which to go about this in your opinion please?
......for instance is it worth or is it possible to lodge an appeal now and add further evidence to that appeal as and when i've spoken to the advisor etc.?
i am feeling a bit snowed under with all the talk of subject access requests etc..and as people know it can be a drain going through the whole process in itself which isn't really what i need but i feel it important to state my case..
any areas which might be useful to highlight in the appeal or particular areas to follow through on?
thanks for taking the time to read and thanks in advance for any assistance you might be able to offer.

Ben