All you have to do to get started with the HPSP scholarship is to contact your local recruiter and they'll give you a contact person for the HPSP recruiters, then the rest is history....
You will need to do a medical physical examination in one of the Armed Forces Medical processing center....
There is no "boot camp" you need to do just OIS (Officer's Indocrination School). OIS is what they call it in the Navy other armed forces have different acronyms. OIS is a 6wks program for you to learn how to wear the uniform, salute, physical (boot-camp like but nothing like the real thing), bed check, etc.....
For more details here is the Navy OIS home page:
http://www.cnet.navy.mil/netc/ois/
There's more in this site than I can possibly explain....
As for your height vs. weight requirement here's another link:
http://www.chinfo.navy.mil/navpalib/news/navnews/nns94/nns94043.txt
Basically, if you're 5'5" Woman you're minimum physical readiness weight is 106lbs and maximum of 144lbs. If you're male of 5'5" stature you need to have a minimum weight of 106lbs and maximum weight of 169.... There are loopholes.... That is you can measure your waist line (above your navel) and subtract your neck line (above your "adam's apple") and if you get below 21inches then you still qualify.... This is how they did it last year and they may have changed the maximum with the waist-neck thing....
BTW, OIS is administered through out the year in certain dates.... most medical types do it in the summer before they start medical school or the summer after first year...
Hope those sites help, good luck