Should we book online (and if so which website)?
If you sure about date and time of the day you want to travel, then it does make sense to book in advance online via official
TrenItalia website, main reason for that is a possibility to buy discounted promo tickets instead of full fare ones. Offer is called 'MINI' and when using TrenItalia website it will look like this
As you can see, instead of full fare (which is 51,5 euro), you'll pay just 29 euro. Also take into consideration that though in case of other routes TrenItalia usually allows to buy 'MINI' tickets quite far in advance (like today up to September 1), but with Rome-Messina the last day of sales is just June 9, while for further dates it's not possible yet.
In case you miss 'MINI' offer tickets, then unfortunately you won't be entitled to a
TrenItalia group discount, somehow for Italians 'real' group is 10 or more passengers, meaning that you'll have to pay full fare.