My flight school experience is >15 years old (USMC), but I had commercial SEL, MEL and instrument, ~1300 hours and did well. I suspect the same principles apply now (for both USN and USAF flight schools). Basically, if you can land a T6 on your first flight, you will be ahead of your peers from a stick and rudder standpoint. The same goes for instrument skills, etc.

However, your best strategy is to not rely on your civilian experience to carry you through flight school. The military is only interested in you learning to fly their way. You should study hard and be at least as well prepared for your flights as the students without civilian experience. Not being prepared for a brief stinks of laziness, and your reputation as a student will be formed and will spread quickly. The instructors will not tolerate laziness. One guy in the class ahead of me was a >1000 hour CFI and flunked out of T34s. The word was he didn't learn his emergency procedures verbatim; thought he didn't have to because he knew what to do generally during emergencies.

As far as the tatoos, why not apply to all services and see what happens? They'll tell you if its a problem.