I will go to Spain for roughly on month. What will be the best SIM-card to buy if I need a lot of Internet access and a few domestic calls ans some SMS?
best in what way?
The company with the best coverage in Spain is Movistar, but they are not the cheapest.
sift your way through this list:
http://www.moviles.com/tarifas/prepago

With "best" I was thinking on 5 - 20 GB to surf for at a low price and at the same time good mobile grid coverage in the Barcelona Alecante area and at the south of Tenerife.

Yoigo usually works out cheaper and has good coverage in cities. SIM cards by law need to be registered in Spain - using your passport or national ID (if EU citizen). You will have to go physically to a Yoigo shop, or rather (and easier) any of the resellers who offer all the brands like The PhoneHouse, and bring your ID.
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