I didn't apply to USNA, but I am a appointee to USAFA who was homeschooled my whole life. I also have many friends who have also received appointments to various SAs. I think for the most part, the same advice applies to homeschoolers. Do well on the ACT/SAT, take challenging courses, prepare hard for the CFA, find extracurriculars that you are passionate about and try to earn leadership positions: these are all pretty much the same.
As a homeschooler, one of the best ways to show you are academically competitive is taking duel-enrollment classes at your local community college; this will help prove you can handle a college level workload, and may even give you validation credit for several classes if you get an appointment. The ACT/SAT is also an important way to show you are competitive academically since they are standardized tests.
I know for many homeschoolers, sports can be a little tricky. It's great if you can get on a team sport, but I wasn't and still got an appointment; you just need to be aware you might need to make up for it in other ways. This will come primarily in the form of extracurriculars (to show leadership) and the CFA (to prove your athletic aptitude). JROTCs are typically school-bound but Civil Air Patrol is a great option to get a feel for the military world.
When it comes to the application itself, especially the nomination process, take some time and prepare for the interviews. Try to anticipate the most common questions you may be asked (Why do you want to serve? Why the Navy?) and start practicing your responses. Depending on where you live, you may have some people on your panel who have some homeschooler stereotypes in their minds (anti-social, introvert, etc), so having clear, confident, and well delivered responses can definitely help challenge these.
When you get to 5 posts, feel free to DM me if you have any questions. Good luck!