Make sure you are speaking with a Medical Program Recruiter, not just any recruiter, as the latter tend to be confused about officer commissioning programs. Although the benefits of the Army and the Air Force HPSP are essentially the same, the difference lies within when you are able to apply. I have applied to both this year, however, am the most familiar with the Army's process. For the Army, they offer both 1 and 2 year scholarships, not to include your internship year. So, for example, I applied for the Army's scholarship in the beginning (fall) of my second year in my program, received it, and benefits will kick in for both my third and fourth year. You are not eligible to begin the process until you have one year of graduate education under your belt, and will become eligible to receive benefits after your second year is complete. It's not that your recruiter is unsure about the process, he just might be unconcerned because it is so early in the process for you. You might re convey your strong interest in the program and ask if there is anything you can complete now even though you're not eligible yet.
As for the Air Force, I'm not certain regarding how many years they will cover, but it must be at least two because I was eligible to apply for this January's board selection. If this is the case, the process is the same as above. I'm under the impression that the Navy is the only branch to offer a 3 + year scholarship, but maybe someone else can chime in about this part of your question.
I've never served on a board, but can relay what I have been told and what has seemed to work for me for the Army. (Still waiting on Air Force results). One thing that they look for is STRONG clinical skills. Although they recognize that research experience is important, clinical activities weigh very heavily in their decision. Additionally, if you have any leadership positions, they love to see that. After all, you're going to be an officer first, psychologist second in the military. Also, you want to make sure your grades are in line, all A's if you are able to manage that. Also, community service seemed extremely important in my interview, and I spoke about it more so than my work experience. I was you foralso told that your ability to support yourself through full time employment, both during undergrad and graduate school also is looked upon favorably. Basically, my suggestion is don't just "do school". Have other meaningful activities outside of school and your personal life. Finally, if you can demonstrate a knowledge of what a military psychologist does on a day to day basis, the variability of jobs you will have in the military, and your willingness to be flexible, you're headed in the right direction.
As far as the packet, I'd need a little more clarification about what you mean.
Hope this helps! It is a long and tedious process, try not to get discouraged.