I can't remember what I used because I got my first passport more than 40 years ago and it has just been renewals ever since. . However, on the official government passport link I gave you, if you go to this other page http://www.ips.gov.uk/passport/apply-first-doc s.asp
it gives a phone number you can ring for advice.
It may be better to check with the people who issue them rather than rely on someones memory!!!
I didn't even know there were two kinds of birth certificate. What's the difference? Mine is of the only type I've ever seen - same size & shape as my marriage certificate, and the same as my parents', and my grandparents'..............