Accidentally bumped into tours to Iseland on the web and prices turned out to be quite attracting so now I am seriously thinking about going on such a trip. Do you guys think that it would be a good idea? This kind of vacation would be something completely new to me.

This is going to be fantastic for you. First of all, as you mentioned it will be your first such experience, secondly the country is extremely picturesque. Read more details about Iceland yours here. I bet it will be very difficult to choose the only one because all these options are amazing. Any tour is a win-win situation for sure.