If nervous about travelling, especially alone, the best way to overcome this is to become familiar with a particular town or region and not have to deal with different languages, customs, ticketing systems, transport systems, etc, too frequently. In your circumstances, as you will likely have about 12 nights on the ground, I would select three places within the same broad geographic area (say max 2-3 hours by train apart). Europe is chock full of wonderful places to visit without crossing the continent. The stress from travel comes from travelling from A to B, finding your hotel, figuring out the logistics, when you're not familiar. Reduce those things and you have a much better time. It is a myth that you'll experience more if you move on constantly - you just experience differently. In fact you are more likely to learn more about where you are visiting if you slow down. Amsterdam to Rome in two weeks is crazy in my view.
So start with the place which appeals to you the most and work from there. Maybe that's Rome? Then pick two other places that aren't too far away. And stay in the city that you are departing for home from, last.
As for booking in advance, I would. Use a site like hostelworld or booking.com. Not having to worry about where you'll sleep will be easier. And the best places sell first. It doesn't sounds to me that you're aiming for the sort of holiday where you will just roam from place to place without at least a rough plan. Although having said that, if travelling in February/March there should be less competition for a place to stay, assuming you don't hit some sort of festival.
If you conclude that you'd prefer to travel with others, you may find a place on a tour but choose carefully. Set your criteria on what would make a good tour for you and seek one out with those factors in mind. Above all, I personally would choose a tour with a maximum of around 12-14 people and preferably travelling by public transport. If you would like some suggestions, we can do that, although most people on this forum travel independently.