How important would it be for a new plebe to go into the academy with some private flight lessons, up to a solo if he wants to be a pilot? Would it be much of an advantage in getting a pilot spot?
If one wants to get a pilot slot, the most important thing is to maintain your health since the standard is rather high. Many students are eliminated each year for a host of medical reasons.
Once your health is under control, the next thing you need to do is focus on is building an "aviation resume". Basically, you need to show the academy that you have an interest and aptitude in aviation. Did you ask for aviation cruises? Did you manage to get any aviation-related experiences with any squadron during summer training? i.e. backseat ride, ejection seat trainer, parachute training, etc. All these experiences give you something to intelligently talk about when you have your aviation interview. It makes it appear as if you have the motivation to get these experiences and that you know what you're getting into.
My understanding is that they now have a flying club at the Naval Academy. Try to get involved with that.
Ultimately, you will have to take the ASTB (Aviation Selection Test Battery). That test specifically tests for aviation aptitude. It's something you can stufy for as I have seen study guides for sale in the Midshipman Store. Here some online sample questions to give you a feel.
http://www.futureofficer.com/links4.html
Your flying experience (especially a private pilot license) will add to your "aviation resume" but will be no guarantee if you do not continue with the other things I've mentioned.
Finally, class standing cannot be completely ignored. That can play a role.
With the advent of Lasik eye surgery, the competitive field gets larger but that is offset by many midshipmen who are turned off by the extremely long commitment - 8 years
after the date of their winging, and the winging could easily take two years. That's a minimum of 10 year s in the Navy,
twice as long for your average SWO selectee whose obligation starts ticking down from the moment they graduate.