To some extent it is possible to largely avoid storms depending on where you go. However on some routes eg Fiji to NZ which takes say 9 days one storm is most likely. It is also likely but not certain that at some point on passage you will go through a gale. More so if you take chances in your planning. You are unlikely with normal caution to encounter a hurricane.
With experience and the knowledge and equipment to handle bad weather you will be uncomfortable, and scared but will most likely survive. Some anxiety is normal but with experience you build up your tolerance level.
And also remember the crew will usally give up well before the boat. So, no matter what, stay on the boat until she actually sinks. As they say, always step up to your life raft, not down. The thing is also, be prepared for the storm, even if it is very unlikely, otherwise if a storm does come, you are more likely to "freak out".
If what you are describing is what you really want to do, you will make it happen,