We're looking for a way to get from Rome to Venice and back in late September.
By "best", we're looking for a combination of
... in approximately that order of importance.
One option is to take the train. I've just looked for a random weekday in September, and there's basically one train an hour in each direction. It's direct, and takes just shy of 4 hours. To get train times, your best bet is to use Bahn.de and search from there. (Yes, that is the German railways rather than the Italian I'm suggesting, but they have a better site and can search basically all of Europe!)
In terms of Cheap, it isn't too bad. It's about €100 return if you book in advance onto specific trains (Mini), rising to about €200 for a flexible ticket (Flessibile).
I'd agree that the train is the least expensive option - especially if you take advantage of the Trenitalia MINI discounted tickets - see my blog article on Trenitalia fares for more information. These tickets can be bought 4 months in advance or the day before - if they are still available.
You also could fly via Easyjet. If you book in advance you can fly roundtrip for under €55. There are additional fees for luggage, etc. but it's still pretty cheap. You will have to take into account the costs of getting to and from each airport. It's an easy bus ride for €2.50 from the VCE airport; FCO is a little more expensive, although Terravision has resumed bus service and only costs €6.
I prefer the Trenitalia site, but I've had a lot of experience using it! For help on trains in Italy, you might read my blog article Riding Trains in Italy. See also my blog article on buying tickets online from Trenitalia. Good Luck!