Did you use skyscanner.com (http://www.skyscanner.com/) for your research?
I just did a test run using March 10 as the departure date, one-way, Venice to Santorini. Many airlines get you to Athens. From there it's Aegean/Olympic only. All options shown have 2 stops along the way, Athens being #2 and #1 being a major city for the airline (Alitalia--Rome, Austrian--Vienna, for examples).
You can click on the "Details" link in the bottom left of the option that interests you to learn more. At the top of the results list on the right there is a question, "Checking bags?" Below that, click on the link that says "Additional fees may apply." You will get a of list many, many airlines. You can click on the ones of interest to you to see their luggage policies.
Be sure to pay attention to the flight time. My little test ranged from 6.5 to 31 hours for that VCE-JTR flight. You can adjust that down on the left side of the page under "Trip duration" and get rid of all the flights that go through odd places, like Moscow.
We flew Aegean from Athens to Santorini on October 16th. There are several price options to choose from. I got lucky and was able to get our tickets during a little sale when we were able to get the highest level of ticket for a price very close to the cheapo plus the luggage fee. We checked our "big" 22x9x14 bags for free/included in the price. By the way, the Santorini airport is the smallest one I have ever flown into on a large commercial jet.
Please note that depending on your date of travel, you might be able to fly one-stop from FCO (Rome) to JTR (Santorini) on Aegean for about 1/4 the price of flying from Venice. The one stop is in Athens. If you can plan far enough ahead to get cheap tickets, it might be worth the time and cost to take the train from Venice to FCO to do that. The cheapest one way price I found for my March 10 experiment VCE-JTR with a reasonable layover and flight time duration (8+ hours) was $623. The cheapest one way FCO-JTR on the same day was $150 for a 4+ hour flight
The DB Bahn search site (http://reiseauskunft.bahn.de/bin/query.exe/en) shows a fast train that leaves Venice Santa Lucia at 09:25 and gets all the way to FCO at 13:52 without a train change. You would have to check to find out the price and verify that schedule. This link to the Man in Seat 61 might help with that - http://www.seat61.com/Italy-trains.htm.