I have made my choice: this site is moving to TotalChoice Hosting. I have looked at many hosting providers, and TCH appeared to be the best choice for me.
I was looking for a hosting provider with more or less the same characteristics as my current provider; I only want a little bit bigger company to prevent problems. In the past I have read good comments about TCH's performance and service, and their prices are incredible. I now have 1Gb of space waiting to be filled!
This is probably the last post I publish on the old server. Once my new account becomes active I will check it, since both providers use cPanel, they are able to copy the whole site for me, and pull the switch. See you on the other side!