Considering most mobile phone operator would require you to install additional software to be able to use their network and that they would most likely cooperate with the authority if asked by the justice department.
You can use any unlocked phone with any operator (assuming it can connect to EU cellular networks of course). Nothing in particular to do, just put in the SIM and it works.
I've never bought a phone from an operator, but I think it's also possible to switch operators without switching phones quite easily, no software update required.
