Thanks, makes sense....
what website or application do I need to run to have my bitcoins in 'my' wallet free from any 3rd party.
There's several wallets you can run locally.
Electrum
Armory
Multibit
BitCoin QT (core wallet)
etc.
Check out
https://en.bitcoin.it/wiki/Main_Page, Lots of info there.
Be sure to do this! Please! Too many people get scammed too often. :/
Unless you have the private key / public key pair, the coins are NOT yours.