1. I was wondering, what's the best way to travel around Europe?

Question

2. I was wondering, what's the best way to travel around Europe.

3. I was wondering what's the best way to travel around Europe.

4. I was wondering what's the best way to travel around Europe?
-------------------------------
Is #1 right? Which one is right? Do we have to use a comma? Do we have to put a full stop or a question mark at the end?

Answer 1

#1 is correct, yes.

You need both the comma after "wondering" and the question mark at the end.