At this point, there is no reason to buy those Regionale (Local), Regionale Veloce or Intercity tickets in advance. Wait until you get to Termini, and buy them there. There is a direct (no changes) Regionale Veloce train that leaves at 14:23 and takes 2 hours, but it's not worth waiting for. Get tickets for whichever one is next and then change trains in Foligno. Be sure to figure out which track your Foligno train departs from. It's a relatively small station but I seem to recall that there's both a Track 1 (Binario 1) and a Track 1N (for North). We missed our train there because I thought 1 and 1N were the same. They're not.
NOTE: These will likely NOT be reserved seat tickets THEREFORE YOU MUST VALIDATE THEM BEFORE BOARDING THE TRAIN. It's really easy to forget to do that, esp. your first day in the country. Because the changeover in Foligno might be tight, I would validate both legs of the trip in Rome (assuming they give you one ticket for each leg). They'll be good for five hours.
And FYI, in a lot of the stations they've moved the validation machines off the waiting platforms and into the subterranean passage that connects the various tracks. And the machines used to be yellow like this but now they're dark green like this
There are trains for Assisi at 11:28 (Foligno), 11:58 (Foligno), 14:23 (direct), 15:40 (Terontola-Cortona), 15:58 (Foligno), 17:00 (Foligno) and later.
Have a great time. Assisi is amazingly beautiful. I'll be there for two weeks in April-May of next year.