Hello, I recently found Arduino and his fantastic world, now that I've done all the "simple" experiments which can be found both in the book and on the Internet I want to devote myself to something more complex as a small robot with 4 wheels controlled by a serial interface that uses bluetooth. Can you recommend a good but cheap bluetooth module?
This depends very much on what you want to do, and you are not specific enough about that. I think the most common robot controller is an Android phone. For this, the HC-05 is excellent, popular, and cheap - about $7. It will also work just as well with a PC.
It has a range of about 10m line of sight. There are more powerful bluetooth modules but I believe they are serious money. It will not work with IOS stuff but I understand it will work with a Mac desktop.
The HM-10 is bluetooth4, and I understand will work with IOS. I think it is a bit of an unknown quantity but the raw module is priced about the same as an HC-05.
The HC-06 is a slave-only version of the HC-05 and just as suitable for a robot.
Here is some background on using HC-0x