Best place to buy bitcoins?
You should generally have a look at the charts:

http://bitcoincharts.com/markets/

A good rule of thumb to judge how much people trust a website is how large is the volume of transactions - the more, the better.

In all regards, Mt.Gox is safe, you can buy there in euros, and I don't think you can bypass the fees. If you worry about the last one, you can try finding someone willing to trade Bitcoins with you that you can trust (which can be difficult at times).