Sea sickness is a very personal thing and is very different for everyone.
Newbies will go through storms without getting sick and seasoned salts can get sick with no warning.
In general, most people will develop thier sea legs and get used to the motion.
By the way, the sense of motion upon getting back to solid ground is usually referred to as "stillness illness." I have enjoyed it in the past, but the more I sail, the less I have experienced it.
An over the counter medication that I have found effective is mechlazine. It does not cause drowsiness, but surpresses seasickness in everyone I have recommended it for. You will need to ask your pharmacist, as it is not on the shelves.