I think you should aim to deploy as many ships as battle allows. It will help with training crew/officers and even ships with useless guns can board effectively or be used as bait.
I am playing US campaign for second time and bought only one ship from admiralty on the first run. Capturing ships is only reliable way to get better ships as admiralty offers ships that are far behind what is deployed by enemy - e.g. I captured Leda class 5th rate as one of my first 5th rates - you can mount on it guns that can bring down SOL which not many 5th rates can do. Best class offered in admiralty for me was 5th rate Diana and it appeared when I had 4 SOL, 2 Endymion, 1 Leda, 1 Diana and 6 other 5th rates.
Buying ships will bleed you of cash you need for crews/guns/research. Captured ship are probably 30-40% of total rep/cash you can get and seems necessary to expand and upgrade your navy throughout campaign.
It might be sub-optimal from cash perspective but I build up roster to 10+ ships and 6 transporters as soon as possible. This allow to fill slots for mission and guarantee success in Point of Interest.