Yes. You can purchase all of your tickets for travel in Italy at the Rome train station. In fact, you can do it all at the electronic ticket kiosk. Karen's suggestion is great. Have your travel itinerary written down. This means that you will have to do a bit of homework first. You will need the origination/destination, date of travel and time/train number. The machine will prompt you in British and will step you through your choices. It will even prompt you through your seat selections. You can also request the Amica fare. You can even pay with your credit card.
Note that the Eurostar trains are the most expensive. If you want bargains, look for the ICPlus trains that are about 25% less. Often times, they can get to your destinations almost as fast as the Eurostars. You can get Amica fares on those trains as well.
The www.trenitalia.com website is very easy to navigate. All fares are now shown on their updated site. (This will be quickly disputed). If you want instructions, I can provide them.