Basel to Wengen

You can buy a single ticket, Basel airport to Wengen at the airport. Remember to exit the baggage claim through the Swiss customs "nothing to declare" door, not the French side. Buses to Basel SBB station are every 7 1/2 minutes, Once in the station check to see the next train connection to Wengen and take it. They are at 28 and 56 past the hour, and some may be direct to Interlaken Ost, then connecting to Wengen.

If, from your other post you are getting Berner Oberland Passes, you will only need tickets tickets as for as Bern, even if you don't get off the train at Bern, Assuming the B.O. pass is active on that day. If you also get Half Fare Cards for the adults, you can get the free Family Card and your kids travel free with you the whole time in Switzerland, plus you get a discount on the price of the B.O. passes.

Just to be specific: the route from Basel is via Bern, Interlaken Ost, then Lauterbrunnen for the little train up to Wengen. Sam mentioned the trains that are direct to Interlaken Ost from Basel SBB. For others you will need to change trains in Bern, or maybe Spiez. So the departure board with the platform numbers may say Brig or some other station rather than Interlaken Ost for the final destination. I would advise taking one of the direct Interlaken Ost trains for simplicity.

Thanks much!