I'm heading to Kuwait for the foreseeable future. What are the best options for communication with back home?

Kuwait is not the end of the world. You will have internet availability. Get yourself a Skype account which will let you talk and see. STAY AWAY FROM THE PHONES as much as possible. Phone bills can add up very fast. And don't forget, there is really nothing like receiving a letter. Take the time to set down and write home. I know it is "old" fashion, slow and such, but when you are deployed there is nothing like receiving a letter, and this goes both ways. I was deployed Kuwait/Iraq for over a year, I used the MWR phones, yea the lines were a little longer and time was shorter, but it was free. I wrote a lot and used e-mail a lot. E-mail, you will access to that as well But just remember, nothing like the old fashion letter.

I was there last year, basically a very garrison environment. your best bet is before you go, look up the installation craigslist on facebook. Then you can contact another soldier and get a wifi puck for cheap. every month its like 20-40 bucks for like 500GB of 4G Data. you can also buy a sim card which does the same thing as the puck but eliminates the need for one. also, the chip can have an installment plan to make phone calls. On post, there will literally be a specific store for purchasing these things, let alone wifi in the barracks. Trust me you will catch on quickly to how it works and have no issues contacting home.

Check to see if your cell phone had WiFi Calling. My Galaxy S7 did and I used it in the UAE on a business trip last March. Called home every day using the hotel WiFi for no cost
Not sure what internet options you may have but it is worth checking out.