this probably depends on the job, I quite like the way it sounds, and it could be that your employer has a fondness for dickensian phrasing, however you don't want to sound pretentious as that can really put people's backs up, so judge your audience; but to answer your original question I'd definately say "to be possessed of integrity..." rather than "possessed by", that sounds a bit scary ;)

I was told when I was little that the easy way to remember is that if you would say "my mother bought some sweets for me" then you say "my sister and me". if you were saying "I bought some sweets" then its "my sister and I etc."- just use what you would if you were on your own (and of course always put the other person first ;)
I don't know all the proper rules but this has always served me well.