For general use I just use a normal, cheap, peaked cap attached to the wettie zip puller (I have sewn a loop of ribbon on the end so it's easy to attach and remove). I bought a few nylon ones from ebay for a few bucks and use them kiting and SUPing.
For the vast majority of SUP surfing it's fine. If it falls off I just put it back on again. It might get knocked off once or twice an hour.
In colder weather I have a swish waterproof/windproof cap that I wear. It keeps my head much warmer than no hat, or any normal cap. If it's real cold I go for the wetsuit hat or hood.
I tried the purpose-made surf caps (with the ear covers) and they just feel too uncomfortable to me.
The bucket hats give better protection but they can be a bit claustrophobic to wear.
The double coat of sunscreen is not a bad idea to get the best performance out of the sunscreen, but there are two problems with that. For a start sunscreen is pretty horrible stuff so it's better to use less of it if you can.
More importantly the 4-hour, SPF 50 thing is a bit over-stated.
www.cancer.org.au/preventing-cancer/sun-protection/preventing-skin-cancer/spf50sunscreen.html