Each country in Europe has its own visa, and depending on the visa you might need other visas for other countries if you want to travel around. So the first question is where do you want to go? Do you know other languages than english? (north countries speak English either as first or second language) Oh, don't forget one country is leaving the European Union in the next years (it might impact you).

First find a couple of places you want to live in and then search for their visas, doing it the other way is going to be a nightmare as you already know.