We will be dropping our rental car off in Basel (driving in from Lake Titisee) the end of June 2017. There are 4 of us traveling, all adults. Our route is to then take the train from Basel to Murren...then back later in the week. Any suggestions for purchasing train tickets?
purchase on Swiss rail site in advance online (one month in advance limit I think)
https://www.sbb.ch/en/home.html
or at the customer service counter at the train station in Basel
Will you plan to take any lifts while in Murren? Maybe check out prices for train + lifts to see whether Half Fare Cards would be worth it for you (you can buy HFC at the Basel train station just before you buy tickets.)
There is generally no advantage to purchasing Swiss train tickets in advance, and your credit card may not work on the SBB.ch website. But as noted above, depending on your plans while in Mürren, you may benefit from a Half Fare Card or other Swiss railpass.
If you will not be riding lifts and simply traveling roundtrip from Basel to Mürren and back, a Transfer Ticket will save you a bit. The regular fare in 2d class is 80 CHF each way, so 160 RT. A Transfer Ticket is 146 CHF. (I did not check the price in $ but you should do that, as this is a pass you must buy before arrival in Switzerland).