How difficult is it to get to the Venice airport from the city?

You take the Alilaguna from Fondemente Nove or Ospedale. It's very easy although it can be a bit of a walk to Fondemente Nove. You say "from the city" but exactly where in Venice will define how you get to the Alilaguna stop.

A cab from the train/bus station area to the airport is about $45. You can also take a local bus to the airport. Or, a vaporetto will take you for $15. It'd be about a 20 minute ride in a cab.

Most likely will be staying near the city center. Is it worth the cost of a private transfer to not have to hassle with luggage on public means?

Not sure if you are aware that the historical city center of Venice is accessible by boat only, except for the Piazzale Roma, as soon as you cross the bridge. A car will not be able to take you in front of the hotel.

The choices from the airport are below:
http://www.veniceairport.it/en/transport/venice.html

A taxi, private transfer car, shuttle bus, city bus, will all take you only as far as Piazzale Roma. From there to your hotel you either take a vaporetto or an expensive water taxi, or you could walk if your hotel is near piazzale Roma.

Otherwise from the airport you can take an Alilaguna boat which stops in several places (about 30 euro/per person) or a water taxi as shown above (for over 100 euro, max 9 people).

How long should I estimate to get to the airport and how early should I get there?
It will depend on where you are staying and the means of transport you take. The taxi from piazzale Roma takes about 20-25 min, but first you need to get to Piazzale Roma from wherever your hotel is. If it's a intra-EU flight, then 75-90 min prior to departure is more than sufficient. At least 2 hours if you fly directly to North America.

Would it just be easier to change my itinerary to not leave from Venice to go to Paris? I can change it to leave from Florence or Bologna if that is easier. Also, how difficult is it to get to the main plaza when taking a train? I know I will have to get a boat. Is it easier to get to the boats from the train station then the airport?

You can take the train to Santa Lucia station, go out the front door, ramps are located at the edges of the staircase. The vaporetto stops are at the bottom of the ramps. Ask your hotel which vaporetto number and direction to take.

Hundreds of people do it every day. Can't see how the hassle of getting to Florence or Bologna would be any less troublesome, and certainly more costly, than getting to Marco Polo. You would still need to get to the Venice train station.

I guess then my question is, is it easier to get to the airport or the train station?

With the number of tour dates and locations that you're juggling earlier in the trip, I can't see rearranging the whole plan now in order to choose a different airport.

If really want to re-jigger the whole thing, then consider Rick Steves' fully guided tours for Village Italy or Heart of Italy.

http://europeforvisitors.com/venice/
The above website has lots of basic info. on Venice and its transport, and is quite detailed.
The Alilaguna boat from the airport to Venice is about E12 one way, unless it's suddenly jumped up to E30 in a year!!
You will love Venice!

As someone else stated, determining if it is easier to get to the airport or train station really depends on where you are staying in Venice. Either destination is not really difficult and also depends on the time of day. The vaparetto to get to the train station can be VERY crowded and some are uncomfortable leaving luggage on deck while sitting below. The alilaguna to the airport is quite easy in my experience has not been jam packed (unlike the vap).
Last fall, my sister and I splurged on a water taxi from our hotel to the train station. Wasn't too expensive and much more comfortable than the vaparetto. You could also check with the hotel to see if other guests are leaving for the airport and share the expense of the water taxi to the airport.