I just noticed that the a manga with that name (fruit basket) is published over here but I dont know if its a good idea to buy the manga (5usd each week....), or do you recomend only the anime?

The manga goes a lot further than the anime - for example, if the manga has 200 chapters, the anime goes only as far as 80 or something.

I definetly recommend buying the manga. Without a doubt.