Having 17 acres with the same type of hilly terrain and being new to tractors as well, I faced the same issue you are. I lurked around this site, read hundreds of posts and finally got the nerve to post my own questions. The advice you have been given is excellent:
1. Ag tires, filled.
2. Tires turned out for additional width/stability.
3. ROPS and seat belt, a must.
4. Front weights if no FEL.
5. 4 wheel drive.
6. Go slow, learn your property's characteristics. Driving over an unseen hole, log, or rock can change your tractor's stability. Go slow!
7. Go up and down but realize that you will have to turn around so plan ahead the areas for turn arounds.
8. Don't mow when it's damp, much less wet.
9. Learn about locking differential, you will be using it.
10. Watch out for thorns, they can flatten your tires.
11. Get a trailer/truck bed/FEL and go find those big rocks, logs that cause you problems, load 'em up, dump 'em out of the way.
12. Starting out, go in the lowest gear up and down and be in 4wd, The 4wd going downhill will act like a brake.
13. Seat belt, seat belt, seat belt.
14. Always have someone else there at home while mowing in case of any emergency.
This is now my second summer of mowing with bush hog. I lucked out and got advice here on Ford 3930 with 4wd, position control, front weights, no FEL. 45 horse at the PTO and tires could be turned out and filled. At first I was paralyzed and I drive 4WD jeeps up/down my hills. A neighbor came by and I got to watch him do it and soon I was doing it too. Used tractor had about 1100 hours and so far its done its job. I cut my yard about 4 times last year and will cut it about 6 times this year as we've had more rain. Anyway, I am no longer as scared of those hills but I still have great respect.
Last but not least, you will eventually learn to love the time you spend getting your land under control. Good luck on your tractor research and ultimate purchase.