Arnaud, you don’t need to spend a lot but I suggest you keep away from any cheaply made sax from China…there are very bad and may not even play. Look for an established brand that offers a more inexpensive student model such as Yamaha, Selmer, Yanagasawa. These companies make some of the best pro models but they also make student models for much less and maybe you can find a used one over there.

good luck
Johnny