Congratulations and enjoy the challenges of getting into a cruising life. My concern is that there is a big difference between taking the course and really knowing how to do it. In four months of practice you are unlikely to get the varied experience you need to achieve your goals in the time you are proposing. Rather than thinking of going to the Caribbean it would make more sense to go to the Bahamas for a season and develop a lot of experience from that. Then come back to US and, if you are still keen, make the upgrades that your boat will need for more adventurous sailing.
I think that having a separate shower on a boat of the size you can afford makes little sense. We have a shower compartment on our 44' and we use it for storage and I suspect you would have to do so as well. Focus on getting a comfortable, reliable, and safe boat. Having a decent head should not be problem, but if you are showering onboard it will be in the head compartment. Most of the time you will find other options for showering.
Heading back to Lake Ontario for this summer. Ainia is back in North America for the first time since 2010. Currently in Long Island Sound.