I used to brew quite often, and since I lived aboard, it was always on the boat. In fact, at the homebrewtalk forum I go by the name "brewonboard".
The trend in the USA homebrew scene is to start with grain, extract, and hop ingredients and get a fairly complex list of supplies together. This gets you "started" and then you "graduate" to all grain brewing, which is complex enough and equipment intensive enough that you don't even want to think about doing it on a boat.
In Australia and Europe, many brew using "can kits" which can turn out shockingly bad, or with very minor tweaking can turn out absolutely great. They require 1/10th the work of extract brewing, and the ingredients are shelf stable.
I HIGHLY recommend the Cooper's homebrew kit. It has everything you need, and with minor tweaks to the recipes the brew turns out great. In fact, I have a coopers fermenter with canned beer fermenting just 10 feet from where I sit now.
Here's the kit, and I've bought from this store before. No complaints.
Coopers DIY Beer Kits
Here's the video that shows the whole process. Easy enough to do on a boat!