Having just made the jump from the RAF (ME background) to BA, I'll chip in a few bits of advice, some of which have already been mentioned.
Get you licence or at the very least get it started. It's not quite the walk in the park you might think; especially if you're balancing RAF tasking, family life/kids and ATPL study. Also, the questions are changing to 'fill in the answer' rather than 'multi guess' meaning that although the BGS question bank is still great, you need to have a working knowledge of the subjects.
Go on a Prep Course (Airline Prep or Flight Deck Wingman) and get your CV written for you. I thought I was in a good position here but it turned my CV writing skills weren't that great! The prep courses give you great advice (and practice) at the group problems and the interview questions.
Revise the company and your answers to the competency questions. Nothing like fluffing your lines in the interview to derail things. Also, the last Annual Report of whichever company you're looking at is extremely useful reading.
Sim Checks. Most people I know (all ME) still went for a practice sim before an assessment. Places and prices vary but I would thoroughly recommend it for two reasons. Firstly, it frees up capacity/allows clarity of thought during the real thing (which is frankly a very stressful day anyway) due to you knowing where to look, what to do and what to say. Secondly, it allows you to get a handle on flying raw beacon nav which most of us in the military hardly ever do.
Finally, the best advice I have is not to rush in to an assessment. Better to give yourself a few days extra to prepare rather than **** it up and have to wait another year to apply.
Good luck in your job hunt.