The train is all very possible and efficient - skip the plane.

The trip from Rome to Florence is indeed 90 minutes, and if you leave Rome relatively early in the morning you can have several hours in Florence. Two possible trains are:

depart Rome 7:30 arrive Florence 9:06
depart Rome 8:30 arrive Florence 10:06

there are also earlier trains, but I was trying to be civilized.

you will arrive at Santa Maria Novella (universally called SMN) and there is indeed left luggage, this recent page says:

You can stash you luggage at the left luggage facility on the ground floor. Cost is 3 Euros for the first 12 hours and 2 Euros each additional 12 hours.

Florence is very compact, and you can easily walk to the major attractions from SMN. If lines are long the Uffizi will probably take more time than you want to use up that way, but there are plenty of other things to do, including just walking around and gawking.

You can then hop back on a train to Venice, including trains at:

depart Florence 3:40 arrive Venice 6:17
depart Florence 4:38 arrive Venice 7:17
depart Florence 6:38arrive Venice 9:17

as well as earlier and later trains. These three do go directly into Venezia San Lucia. From there you can hop on a water bus (dock is right outside the station) that will take you directly to Piazza San Marco in just a few minutes. Or, splurge on a water taxi as you'll have had a long day.

The walk from the station will take much longer than the 5-10 minutes suggested by another poster, will be difficult with luggage, and you can certainly plan on getting lost more than once (part of the charm of Venice, but not when you're tired and dragging luggage behind you).