hi Kiki !
I don't know if you should worry... it depends on how much money you have in your bank account. If money is an issue, you should at least know how many days total you'll spend in Western Europe, since it's so much more expensive than in Eastern Europe.
Another important point is that you'll be travelling in the high season. Hostels will be crowded, so yes, it's better to think a bit ahead and book your room. No need to book everything before leaving, I believe one week ahead is enough, unless you really don't want to sleep in hostels that are a bit off the center.
You want to travel from Paris to Rome by train, then from Rome to Eastern Europe by train ? Do you realize that those are looooooong journeys !? You could hop by RyanAir for a few Euros and save time.
Is this helping ?