You have a good start there. here are my suggestions:

1. I would get the DX6i radio instead of the DX6, if you can afford the DX7 is better, or the 9303 is even better yet. The other radios have extra features that you will find very useful if you stick to helicopters. Make sure you purchase the heli version of the radio you pick. Go without servos, because you will want to use the HITEC 65MG servos (x3).

2. No, you need to purchase a gyro. The Futaba 401 seems to be very popular as an entry level gyro. Pair that up with a 9xxx series servo (I can't recall the number) and you have a solid tail set-up.

3. For batteries, I would go with 20C or better discharge rate batteries. Those you have listed are 15C and they are good for hovering and flying around, but if you intend to do some aerobatics, those will be marginal.

4. The heli package includes ONE (1) battery. The extra batteries are listed on your battery link. You will need a lipo capable charger. Most of us recommend one that you can read the current going into the pack, that way you can calculate pack discharge, but that is not absolutely necessary. You will also need a battery pack balancer to keep your lipos in top shape.

I have this balancer: [link]http://www.amainhobbies.com/product_info.php/cPath/2_384_388/products_id/8604[/link]
And this charger: [link]http://www3.towerhobbies.com/cgi-bin/wti0001p?&I=LXMAJ0&P=ML[/link]

Rafael