What's the best harness?

My Beardie Oscar has a very sensitive throat, even a very light pressure on the collar seems to make him cough like he has kennel cough - which he did have a few years ago. I'd like to use a body harness - but is this even feasible with such a very, very hairy dog?
What's likely to be the best one to try and what measurements do I need to do to find the right size?
Thank you!
Beverley Cuddy
Editor, Dogs Today