1. I would suggest getting a bitcoin wallet on your desktop/laptop they are the most secure. It will give you a bitcoin address that you can receive bitcoin on.
I would recommend the bitcoin-qt wallet it is the most common and works on pretty much any OS
http://bitcoin.org/en/download2. The wallet will give you an option to backup your wallet, this will make a wallet.dat file. This is not so much a copy of your wallet but more of a key to prove to the network that the wallet is yours. If your system ever dies or you get a new one just install the wallet again and drop your backed up .dat into c:\users\[name]\appdata\roaming\bitcoin\
3.
4. I have never tried to buy and btc as of yet, so i wouldn't know the best way :/