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It really depends where you live and what is available. Generally, in terms of broadband, best translates to fastest and most reliable, and the general consensus is (in the US) Verizon FiOS fiber-to-the-home broadband internet. However, that may not be available to you. Other places in the US have Comcast, Charter, Time Warner, Cablevision, Cox, and RCN for cable, and for DSL, AT&T, Verizon, and (to a lesser degree) Qwest are the most well known.
It really depends on where you are at. What city you live in, what services are available in your area, and sometimes what state you live in will dictate who your service provider is.
By 'live messenger' I guess you mean 'Windows Live Messenger', and if so, no, you do need an internet connection, but it does not have to be a broadband connection.
I guess this depends on where you live as you did not say where that was. I live in Central Florida an their triple play of phone, internet and tv service is available for a limited time form $84.99.
broadband connection
I use sky broadband and i have xbox live, and i also live in the country. It seems fine to me when im in the middle of no where, so i expect it should be alright for you.
To a certain extent, the best service available may be dependent on your area of the country (or the world, if you don't live in the United States). You can find out more by searching your location and "wirdless broadband." AT&T offers something called "U-Verse." This is widely available all over the country.
no
An Xbox live gold card and a broadband Internet connection.
Broadband connection and an Xbox live gold subscription card.
Broadband. Ethernet cord.
you have to have broadban or better