I think I understand the basics a bit better now. Get a desktop wallet sounds like good advice.
Thanks to all who replied.
Very important is that you read and research very well everything. With Bitcoin there is no much room for a mistake. For example, transactions are irreversible which means if you send your coins to the wrong address, you pretty much have lost them.
So before you do anything, make sure that you understand it. It you don't understand, always ask questions and we will help you.
Yes, try Multibit wallet or Electrum wallet. These are light wallets, the, don't require that you download the whole blockchain. Make sure you understand the wallet before you send all of your coins to it. And make sure your computer is relatively malware and virus free. You also have great tutorials online on how to use these wallets.
Another thing is, when you set everything up, always test the system with a little amount of your wealth. I do this all the time when I do something new even though I have a lot of experience. So send 0.01 BTCs to your wallet and then try to resend them back so you see that you control your wallet and not other way around.
Hope I helped!
Cheers!