When you turn on the Xbox 360 you'll come to the "DashBoard". It is a menu with various pages and you change pages by pressed Left or Right. One page is the Xbox Live one. Here you can create an Xbox Live GameTag/Account. Just remember to change your name/gamertag they charge you money, so try to pick a GamerTag you can live with. Anyway with your new Xbox you get 1 free month of Xbox Live Gold membership, after that you either pay a subscription fee or it goes down to Silver.
The Silver and Gold difference is primarily one thing, multiplayer gaming. You can't play games with other people over Xbox Live unless you have Gold.
Anyway when you sign into Xbox Live one of the pages is the "Marketplace". This page will let you download stuff. Some stuff is free, other stuff you buy. You can download lots of free game demos, game trailers, etc. You can also download stuff you pay for, like Xbox Live arcade games. These include 3D Mini Golf, Double Dragon, Street Fighter 2 Hyperfighting, Doom, and many more.
You can also pay to "rent" High Definition movies. The movies are 720p and I'm not entirely sure how it works other than Movies after you download them, you watch them and after the first watching or something you have a limited amount of time where you can watch it again.
You can also download TV shows too. TV shows are ussually if not always keepers. You download say an episode of South Park, and can keep it and watch it whenever you want forever.
Definitely make a Xbox Live account to browse the marketplace and download game demos.
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AlexMax, the Elite version has been proven not to be immune to the Red Lights of Death fault. Some Elite's appear to have improved cooling now, however so do some premiums. The one thing you should try to do is keep the Xbox 360 cool. If possible don't play it in a room that's rather hot, make sure it blows the hot air away from the unit and isn't stuffed in a entertainment cabinet's shelf with no way to get rid of the hot air.
Even if you aren't that careful or you are and it breaks down, as long as it lasts long enough for the 65nm chips to be on the shelves so you can replace it with that, you should be ok. I'm on my 2nd console and hoping it lasts long enough so the 3rd will have 65nm chips. Honestly I just expect this console to die. It already has begun to freeze randomly on Rainbow Six Vegas.