Most (if not all) of the trains from Rome to Assisi will be Regionale or Regionale Veloci, so there will be absolutely no price difference whether you buy tickets online or buy from a Kiosk or staffed ticket window at the station. Regionale tickets purchased online will be pre-validated so you won't have to validate, but trips must be started within four hours of the departure time listed on the ticket.
I find it just as easy to buy Regionale tickets locally, usually from a Kiosk. However, as someone else mentioned don't buy tickets ten minutes before your train departure, as there may be a queue at the Kiosk, or the Kiosk may be broken. I often buy Regionale tickets the day prior to travel so that I don't have to deal with that when I'm heading for the train. Don't forget to validate!
If you want to buy advance tickets for any trains in Italy, either Trenitalia or Italo, I'd recommend using https://www.trainline.eu/ as it's very user friendly once you're registered on the site, and they have a smartphone app.