Low Bandwidth options

I’ve got a bit of a conundrum and hope someone can help. Later this year I’m going to Antarctica, and before I do, I’m trying to ensure everything on my Macbook Air is as set up as it can be. My problem is that I have a very, very strict data allowance of 30mb and then the connection is cut off. All I want to use the net for is sending emails to friends and family back home. Is there some way of blocking every single other incoming and outgoing net connection? Any thoughts on what’s the best browser/webmail combo that uses the least bandwidth? What’s the most accurate traffic monitor? I have no problems setting up new accounts and am planning on only using plaintext emails to conserve every byte I can, but even if I manually shut down/uninstall anything I know uses data, I’m sure there are background processes sneaking in there somehow and it’s those I’m concerned about. (I feel like I've lost over a decade here, dialup was really no fun at all)