Several questions about Cinque Terre

Are you only looking to go to the CT? Venice is easy by train, if it were me, I'd fly into Venice, spend a couple nights there, then move on to CT.

Do you have 7 nights total? IMO, I would do:

Venice 2n
CT 2n
Florence 3 n

Or do the CT as a day trip. I was there for 3 nights, and I loved it, but probably would have been happier with only 1-2 nights.

Oh, and train, definitely.

Also, consider doing the Venice, Florence, Rome Triad. I personally like all of those more than the CT.

JE,

Regarding your questions.....

• Pisa is probably the airport I'd choose. It's relatively close so easy to get to the Cinque Terre via the frequent trains.
• Yes, it's very easy to get to Venice, but that will be a longer travel day since you're pretty much travelling from one side of the country to the other.
• Travel by train is by far the easiest and quickest method, especially if using the high speed trains which run at up to 300 km/h. Many routes require "changes" so you'll have to get up-to-speed on that. Also, there are some potentially expensive "caveats" to be aware of when using trains and other public transit in Italy. If you need further information on that, post another note here.

Which if the five towns are you planning to stay in?

The priorities are CT and San Gimignano. Maybe I fly in and out of Florence or into Pisa and out of Florence.

Florence and Pisa airport are not that far from each other, either can work so go with the better times and rates for your trip.
Despite having a major train station and being a very popular city, Florence's airport is small and flights are not that common. Flights into and out of Pisa are usually easier to find.

San Gim and CT while not that far there is not going to be a great way to travel between them on public transit. Can be done just not directly, you will have to use Florence or somewhere similar as a hub to make the connections happen.
Would be easier to take a car but parking in either place is not good so if driving may be best to park in La Spieza and train to Cinque Terre from there.
I would not rent a car only for this one drive, would be too costly to do so ; only reason to go with a car is if you envision exploring the countryside around San Gimignano or are staying outside of the town center itself at a farm or similar.
While in the CT the car will not be used.

Think Venice would be a long day trip from either place, again no direct route so need to use Florence or somewhere as a hub, think would be better to save Venice for a future trip if you only have 7 days.
Spend 3 nights in the CT, 4 nights in Tuscany. Staying in San Gim is fine for those 4 nights but I assume you will take a couple of day trips or be driving around. I imagine day trips to Siena and Florence are 2 options from San Gim if you don't have a car.