You can also look at apps like The Trainline to see all the options in
one place. They charge booking fees and have potential issues (how you
get refunds from 3rd party, etc.). I just decided for me, the fee was
a small thing compared to having my brain swizzled with all these
different train lines in every country. I'm planning a UK trip right
now with lots of train rides and I just gave up. I want all my tickets
in one spot, one app, done. LOL I haven't done my Italy train tickets
yet, so maybe there's a different all in one train app that is
Both the Trenitalia and ItaloTreno websites and apps are so simple to use I don't see any reason to need a third party reseller to organize your tickets in Italy. For simplicity sake we most often just book with Trenitalia as we usually have a mix of fast and regional trains. (ItaloTreno runs only fast trains).
I can see some benefit of Trainline if you are traveling in multiple countries and have many different train companies to deal with- but I'd still probably not use. I prefer to avoid third party resellers/sites.
OP has indicated that they only need tix for a few certain routes- all served by Trenitalia, so why not keep things simple and use just Trenitalia?