There are a range of types of train, depending on destination. On secondary lines you will not have a choice and will have to take a regional or inter-regional train. Sometimes these trains do not have a first class section; one feature to check is that many have declassified first class sections (ie., former first class compartments). Thus you can travel in first-class comfort at second-class prices!
Unlike many countries depending upon revenue for their public transport, Italian trains and buses have a fairly simplified ticket system. First class and second class sections are normally available in all but the most regional trains; first class is not that more expensive.
Sometimes it is not possible to avoid travelling first class, since there are a number of trains that are exclusively first class. I find this rather annoying - while these trains have optional seat reservations, it is also possible to travel on them with a reservation. Thus, we travelled in December 2006 with a reservation but since the train was so crowded with people lacking reservations, it was impossible to get to our reserved seat. Additionally, you have to be completely heartless to ask an Italian family, complete with grandmother and baby, to vacate your seat!