I'll take a quick stab at this, but really this is a good conversation to have with your instructor over a beer
1. Be conservative. Don't push your training. Work up to things.
2. Good skills - work hard every dive on buoyancy. Consider a peek buoyancy workshop (where you and a couple others put some energy into thinking about and practicing the skill).
3. Monitor your air supply and don't push it. Make sure you always have plenty of gas for a safe ascent, a safety stop, *and* to be able to handle nasty conditions on the surface. I like to call a dive at 1000 psi (on a 3000 psi tank) instead of the more common 500 psi, just so I have a little more reserve.
4. Stay well away from the NDL limits for recreational diving. They're the point where you statistically you'll start having problems. Consider subtracting 10-20% off the NDL time.
5. Ascend rates - one of the biggest problems I see with newer divers is fast ascent rates. Consider stopping for 1 minute every 10 feet during your ascent.
6. Overhead environments. Don't. Not until you have lots of experience and training.
7. Equipment - dive only with high quality equipment that has been regularly serviced. Rental gear is *ok*, but owning your own is much better. There are regular articles about people getting into trouble due to equipment problems.
8. Buddy - dive with one. A good one, that you know and trust. The blind date approach is more than a little scary.
9. Health - it's incredible that people still go on dives with colds, the flu, etc. Don't do it.
10. General physical condition - diving should never be the most serious exercise you get. Consider bicycling, running, swimming, etc. to go hand in hand with diving.
I hope at least some of this is useful. Your mileage may vary. Best of luck, and welcome to the sport!