Yup, Marines have them too. I think you'll get a lot of advice online that says "worry about being a good junior officer first", but I disagree (not completely). If it's something you're really interested in, you should look into it now. They're often pretty competitive, and you'll probably have to do some career planning to get there and to fit them in. So, you need to be a good junior officer, BUT you may have to fill certain wickets too. Plus, you sort of have to double qualify: you have to get past the Navy (or Marines), AND the school has to accept you.
You're pretty specific about PMM programs, which I think are detailed in NAVADMIN messages. Snoop around for MARADMIN messages on the same subject; they'll list references on the message, which you can then reference further. Pretty much any program is going to require a "payback" in terms of years of service, but there are many other ones (besides PMM) in which the Navy pays for your graduate degree. I think being a Company Officer at the Naval Academy is one. They send you to University of Maryland for a year, then you're a Company Officer at USNA, then they've got you for Dept. Head (or whatever's at that level in the Marines). Also, a ton of people go the "cushy shore job" route and get it on their own time, either at their own expense or using the GI Bill. In any case, I personally think you're smart to ask for personal anecdotes on places like this, look up the actual references so you know the requirements and level of competition, and sketch out your career, always remembering that things might not work out the way you planned in the military...but they always work out!