You can get from Venice to the CT by train either via Florence or Milan (with connections). The times are similar, and I don't think it makes a huge difference whether you go from Venice to Florence to the CT or Venice to the CT to Florence. Sometimes the departure time of one vs. the other just works better. Just look at the schedule for the day you'd be traveling. Last May, I traveled from Venice to Camogli (on the riviera, north of the CT) via Milan, but because it was a last-minute trip, the regional trains (one extra change, less than an hour longer) were a lot cheaper than the last-minute fares on the faster trains. Keep that in mind, too - the cheap fares tend to sell out early on those fast trains. Waiting til the last minute to buy tickets means either higher expense or taking the regional trains like I did.
If you to go Florence first, then the CT, you'll have a longer train ride back to Rome after that, for what it's worth.
See:
www.trainline.eu (Trenitalia and Italo trains)
www.trenitalia.com/tcom-en (Trenitalia trains only; must spell stations with correct Italian names)