If you buy the high speed train ticket and pay extra 2 euro

to select the seat per person, then the seat you selected during the booking process is assigned to you rightway; if don't want pay that extra 2 euro, then the system will assign a seat to you, you still get the seat for sure, but cannot choose where you want to sit/or sit together with your family, just like you book air flight ticket those days. Note: I'm ONLY talking about to book the high speed train ticket in Italy.

I prefer to book the ticket on train operator's web site directly, not via 3rd party web site.

When I booked the Italo's ticket online before I leave from United States, my credit card transaction went through smoothly, but to book TrenItalia's I have to use PayPal (somehow my credit card does not work on their web site), maybe just me.