Realistically- the better the helmet- the better for you!
Goggles are a good idea- but depending on the surface you are sailing on glasses might be ok.
As snow tends to be a bit patchy around here, I cant really comment on the pro's and con's of skiing and snowboarding helmets

I am using a skateboarding helmet and safety sunglasses on grass ovals and dry lake bed, on salt lakes I recommend using goggles- salt in the eyes slows you down.
Sometimes on the lakebed, during dry and dustier conditions goggles are best and something to filter out the dust when breathing helps (simple cowboy style neckerchief/ cotton dish cloth works well for us) again- on salt lakes, the neckerchief will stop the salt and sun burning your lips and face.
personally- I dont think regular bicycle helmets are quite up to the job- but then- I have used them myself

I would regard skateboard "hard shell" helmets as a minimum.
Skateboard helmets have a tougher shell than a flimsy bicycle helmet and cope with boom hits much better.(bike helmets have a thin skin and fall apart)
Motorcycle helmets are better again- but (in my experience) are not very comfortable for the type of lying prone position that we usually have in landyachts.
I have been meaning to fit a better angled sunvisor on my skateboard helmet, as the angle from lying on my back in the landyacht leaves no shade for the eyes.
Easy fix with some plastic probably from an icecream container, and some velcro.
Best bet- borrow a couple of different types of helmets and try them when you go sailing.
All the best- and happy new year
Stephen