Bit of a bone question here but as I've never applied for my own passport before I thought it's better to be safe than sorry! Applying for my first adult passport, I had one as a nipper which is now expired. Am I applying for A) Renewal of my passport or B) My first passport (since it's my first adult passport)? Thanks.

B, applying for your first passport, all explained here

Applying for your first adult passport : Directgov - Travel and transport

Renewal.

Brilliant mate, ta.

The table on the back of the instruction book has a section for 'Getting your first adult passport' since I'm a renewal is this still me?

Google renew British passport. The page for passport info is a combined site where the Brit government has combined plenty of sites into one. Pick the passport area.
They are slow to be processed so if needed in a rush do pay the extra. From my own experience I had to do mine through Brit Embassy in NZ. It took so long I applied for an emergency travel passport in PNG. Avoid this little white document like the plague. It costs a lot and has very specific travel route printed in it and dates you pass those airports. If you travel a a lot get two passports, the immigration people like to use whole pages whenever possible. On a sidetrack, the lady in the Brit High Commission at Port Moresby did look rather flash. Nice face and large lungs.