How should I send my bitcoins to my wallet from coinbase I just bought Bitcoins with Coinbase site, and as I read about bitcoin, everybody say I shouldn't let my bitcoins in Coinbase, as I don't have the private keys.

So I opened a bitGo Wallet, and try to send some bitcoins there, but If I want to send 10 euros, it cost me 31.22 euros to send it... 

I don't understand it. Can anyone help me understand why ?
If you only have 10 euros in Bitcoin, it is currently not worth sending to your wallet. The current Bitcoin transaction fees average around $50 USD today. You can see the chart here. This is because there is an enormous amount of Bitcoin transaction, but only a few transactions can fit in the 1mb block.

If you had much more money, you should definitely send them in a wallet you own the private keys. Some exchanges like Mt. Gox closed and millions worth of Bitcoins were lost. There's a lot of fire right now in the Bitcoin community, so owning your coins is a good start.