Thanks a lot for your replies guys. I have good news
I've had great results from my first try at polishing.
I used some products from the brand Riwax. I got a shampoo, and a product they call Polish & Wax. I started off with the bonnet, where most of the damage had occured.
It worked, bird ca-ca stains were gone. I couldn't believe the shine. I just had to polish the car all over. Very satisfying feeling when I was finished.
I've learned a great deal about polishing & waxing in the meantime. My car has collected a couple of scratches and stone chips, and of course the polish won't make them disappear, but overall the car looks great.
I'm currently piecing together a very nice kit from Meguiars, which will include everything I need, I will treat my bella to a good cleaning for her 10'000 kilometers report, in a couple of weeks.
Thanks a lot for your help and good advice guys, I am happy again...so happy in fact that I got 210 kms out of 60 liters of 98 unleaded