I need to buy a smartphone, my first, and I'd like a very basic and cheap one. ?

ZTE is a good low-priced brand.  

Mine came from Consumer Cellular for $40. 

you could try amazon, they sell everything

Europe and a lot of the rest of the world uses GSM (Global System for Mobiles) cell phone technology, where the USA uses both GSM and CDMA (Code Division Multiple Access), Sprint and Verizon use CDMA but all the others use GSM, so for your phone to work in Europe and a lot of other places you will have to get one that will work with GSM, you can get phones at Sprint and Verizon that will work on both, you may have to get an international plan as well though most major carriers have international partners now