I can only speak to what USNA recommends for unsuccessful candidates:
(1) Find out what was lacking in your package. Ask CGO directly.
(2) If it's academics (classes, grades, SATs), attend a regular college (can be community college) and take to the greatest extent possible the courses a plebe takes -- Calc, Chem with lab, English, World History. Doing well in these classes at a college level helps demonstrate that you can handle the work at USNA.
(3) If it's something else (athletics, ECAs, leadership), discuss with CGO and your BGO ways to work on those while still doing #2 above.
Some unsuccessful candidates believe that they need a more "structured" environment to help them improve enough to be accepted to a SA. That could include, for example: tutoring, study skills, time management, test-taking strategies, physical training, etc. In some cases, a prep school may be able to provide help with some or all of these things.
I'm sure there are many good -- and some bad -- prep schools out there. Before you plunk down your $20,000+ to attend one on your own (non-sponsored), consider some of the following:
(1) What can/will they provide that you can't do for yourself and does this address a major weakness that you have?
(2) Are any credits you earn transferrable to a SA or the 4-yr college of your choice? If they are affiliated with a particular college, is that where you want to go? IOW, if for whatever reason, you don't end up at a SA, will that year have been "wasted" in terms of academic credits?
(3) What does the SA of your choice say about the school? NOT what does the school say the SA says about it. If you are unsure, check with the CGO (or equivalent). They obviously can't make recommendations but they can indicate if there is any "official relationship," how many students were offered appointments over the past few years, etc.
There is no single right or wrong answer. But, there is NO guarantee that you'll be offered an appointment even if on a sponsored scholarship -- without one, you take your chances. As always in life, if it sounds too good to be true, it probably is. So, do your research carefully -- a prep school may be exactly what you need to get into an SA or may simply be a waste of time and money.