Cheapest way from airport is to hop on the bus to Piazzale Roma where you can jump on a vaporetto. More expensive and quicker way is take the Alilaguna boat from the airport or even more expensive and fast would be a private water taxi.
The vaporetti prices can be found here: http://www.actv.it/english/navigazione.php?pagina=tariffe_vaporetto
Sant'Elena is a very nice area of Venice with lots of trees, green grass, wide open spaces, parks, playgrounds. It's very different from the other areas of Venice. We've stayed in both San Marco and also the Dorsoduro areas on previous trips and walked to Sant'Elena. It's like an oasis from the busy hectic tourist scene. If it were my first time in Venice I would probably rather be located right in the thick of things...not Sant'Elena. However, now that I've been there a few times I think the tranquility of Sant'Elena is quite inviting.
It's definitely a very do-able walk from Sant'Elena to most places...however NOT with luggage.