Just use the official company and not resellers. They will charge you more and not offer all the solutions that may be available.
Only Trenitalia serves your routes.
On its website, click the UK flag first for English, enter Roma Termini, Verona Porta Nuova and Venezia S Lucia as appropriate, and enter your 'hour' of departure or just '5' for 05.00 to see all trains.
Rail Europe and Italiarail are both agencies = ticket resellers, not train operators. For best prices, you need to buy directly from the train operator, which as you already know is Trenitalia (Italian State Railways, also FS).
Rail Europe - which actually belongs to SNCF, i.e. FRENCH Railways - sells tickets in English-speaking countries at a ridiculous mark-up: I have never looked for Italy but I know they sell a ticket that costs €14.10 from Belgian Railways for the price of 29 USD = €21 - which is a 50% mark-up!
Italiarail, on the other hand, passes on the same mini-fares you can get from Trenitalia and does not charge such a high commission - which, in any case, you can get back if you e-mail tripadvisor(at)italiarail.com with something like "booking fee refund" in the title line (also other e-mail addresses for other travel websites, e.g. seat61(at)italiarail.com). The Italiarail site can be much easier to use than Trenitalia's, and it does offer you the advantage of paying in your own currency.
I suggest you read "How to Buy Train Tickets for Italy" on here: http://www.seat61.com/Italy-trains.htm
Italiarail good for buying Super Economy no exchange no refund tickets, or if you find the Trenitalia website impossible. But otherwise, its exchange and refund conditions are inferior to Trenitalia's.
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