What to look for when buying cyclo-cross or road bike under 600eu/650usd?
Cyclocross is a type of bike race, which means that most true cyclocross bikes will be expensive, as they are built to win races. You won't find much for that price range if you buy new. But racers are always looking to go faster and get new gear, so consider getting a used bike. You should be able to find a very good used bike for that price.

Also consider looking at touring bikes. They are built quite similar to cyclocross bikes. Except that they are built at little stronger because they are built to carry more baggage. They also have mounting holes for racks which will come in useful for commuting. Many cyclocross bikes don't have the ability to mount racks because racks aren't used for racing.