You'll want to use the official site of Trenitalia which is the state train company of Italy: https://www.trenitalia.com/en.html
Use the Italian city names for best results when searching on train sites: Roma for Rome, Firenze for Florence etc. They also have an app for use in country that also let's you track trains in realtime and validate tickets etc.
.Italo website is here: https://www.italotreno.com/en and they also have an app.
Fast train tickets with assigned seats do not need validation and those are good only for that train and that seat. As others have said the service is largely the same between the two companies. There are also classes with each train that are largely the same. Some people have a strong opinion on which seats are most comfortable but with short trips of a couple of hours I can't say I think it really matters. When you book early the differences between classes is usually just a few euros. I will sometimes pay a couple of euros to go from standard to premium on Trenitalia - which is 3 seats across versus four - but unless it is a very long trip paying full price I wouldn't the 20e for it or for any upgrades beyond that.
And no, there is no way to know for sure the direction of train travel when you book a seat.
The man in seat 61 is a really good basic primer on Italian train travel: https://www.seat61.com/train-travel-in-italy.htm
Have a great trip,
=Tod