What to look for when buying cyclo-cross or road bike under 600eu/650usd? I really want a fast bicycle, that I could use in winter, summer, rain &amp; snow to commute to work. After some research I found out that there is a cool option of cyclo-cross bikes that are build for speed, but can have better tires, mud protection... (winter/rain).

I would use bike mainly to commute to work, usually would ride bicycle on city roads (no off-road or mountain driving). Danish weather is usually moody (rain, little ice here and there) therefore I want something that could have more durable and stable tires.

So again, i came across cyclo-cross bikes and now I was wondering if it is possible to buy a good one under 600eur. Talked with colleagues that have great bikes and they started talking about gears, breaks, handles... and in the end of conversation they summed up that the bike will cost at-least 1500eur. 

The thing is, it would be my first 'good' bike and I am not going to go pro or whatever (just commute in different weather). So I decided that I can only spent up 600eur and then I wonder what is the most important things to look for in the bike. 

I appreciate any suggestions, tips, help or direction where I should look for bikes to buy/order. Thanks! :)
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.