I can't comment too much on availability but I have travelled on Trenitalia using both a pass and buying individual tickets. Usually the queues at ticket offices (to convert your pass into a ticket) are quite long. Also in Italy train stations can attract a number of undesirables so I try and minimise my time there. For these reasons I now book my tickets in advance.

Another tip that you may not have thought about - Italian side walks are "cobblestones" so very unfriendly to your roller suitcase. So I strongly recommend travelling with a backpack or at least choose a hotel very close to the station to minimise your schlep. These aren't often the best and most touristic of areas, but it's easy to get your suitcases to the hotel then do the longer walks without the hassle of your bags.

Enjoy!