My daughter, as well as Chip, just went through this process.
She applied only Army ROTC - some advice for that:
Check out schools the spring of your junior year. You can put 6-8 schools on your list, I forget the actual number, but fill up the list to keep your options open. Put schools on your list that have your desired major and do not fill your list with "reach" schools.
Remember it is possible to be awarded a ROTC scholarship and not be accepted to a school.
Complete your application and have your guidance office send in your 6th semester transcripts as soon as they are available. Usually right after you get your report card.
The application itself is easy and all online.
Do the work early because the first round goes out in November. My daughter was offered in mid-October at her interview, got her letter of intent about 2 weeks later. It is a relief to have it done early and a Plan B underway.