IMO if you get PDZ it will ruin your 360 experience. Get Graw or COD2. COD2 is possibly the best SP FPS game I have played in a long time. Really Really good. GRAW is a good SP game and a quality online experience. A few of us play together regularly on live. I have to say most people I play with come back for more.
You already have a wireless controler in the Premium package. The second would be for a friend I assume. Also a plug and play charge kit is a fairly good investment (and a second battery for the second controler)
You should also get live. at £40 per year it works out at £0.11 a day.
An Xbox without live is like lemonade without sugar.
The thing that a lot of people without live do not realise is that it is a completely intragrated system. You sign up once and choose your Identity. That identity is shared accross all of your games, unlike say the PC or PS2 system where you need to create your identity for each game. You have a friends list, which lets you know who is online and what they are doing. You can send them a game invite or (if you are playing the same game) you can join their game at the click of a button. Also with some games eg GRAW. you can have a guest sign in and play on live with you, split screen (they can also sign in using a seperate Live account).
