I now have 1 BTC in my wallet

Thanks

So I'm going to buy my first Bitcoin but I'm a bit nervous about it. So I got the MultiBit client because the Bitcoin client seems kinda slow (downloading blocks etc).
Let me get this right: When I buy a BTC from a website it asks for a bitcoin address, which is your wallet private key I guess, which I can find in MultiBit under: "Request" -> "Your address".
Is that all correct?
Anything else I should know before buying a Bitcoin?
Thanks!