Barcelona to Interlaken

At Basel airport, the buses to the SBB station are almost continuous. Like every 7 1/2 minutes.

Basel airport to Interlaken Ost, 2 hours 23 minutes, 65 CHF, departures every 30 minutes, one change.
Geneva airport to Interlaken Ost, 2 hours 56 minutes, 75 CHF, departures every 30 minutes, one change.
Zurich airport to Interlaken Ost, 2 hours and 17 minutes, 75 CHF, departures every 30 minutes, one change.

But if you go from Zurich via Luzern, which is more scenic:
Zurich airport to Interlaken Ost, 3 hours and 8 minutes, 56 CHF, departures every 60 minutes, one change.

Fly Barceloa to Zurich; then take train from airport to Interlaken via Luzern is my vote.

Thanks for the well articulated response Sam. Jazz, I'm curious what is the basis for your suggestion? Is it because this would be the most scenic route?

Last July I took Zurich train from the airport to Luzern stayed a day and then Luzern to Lauterbrunnen via Interlaken Ost. It was quite scenic with out it being one those designated scenic route tourist trains.

The train between Luzern and Interlake Ost is sometimes referred to as the east end of the Golden Pass route. It will go over a high Alpine pass (Brunig Pass), through Meiringen (where they invented meringue) and near the Reichenbach Falls, where Sherlock Holmes and Professor Moriarty fought to the death.

Barcelona to Interlaken is FAR too long a train ride (12+ hours). Just fly to Zurich and then train to Interlaken. We did this route in reverse in June 2017. Stayed in Murren then departed early from Murren to Zurich Airport and boarded the plane to Barcelona.

You should definitely fly -- be sure to check low cost carriers like EasyJet and Vuehling. The cost and net time should be the same from BCN and Basel or Zurich (on to Interlaken) -- I would choose Zurich as the others said, for all the same reasons. The route from Basel just isn't as scenic.

I did think there has been any question that the OP is flying, just a question of which of 3 airports in Switzerland to arrive at.

just a question of which of 3 airports in Switzerland to arrive at.

Precisely, and as Sam's post said, all three airports are roughly the same time to Interlaken and the Jungfrau area, just pick whichever flight has the best cost/time of day.
And, if you choose to fly to Basel or Zürich, and it is early enough in the day, choose the route via Luzern instead of via Bern. The Luzern route takes 1 hour longer but is much more scenic.

Map of Swiss railways, which might help: https://www.sbb.ch/content/dam/infrastruktur/trafimage/karten/karte-sts-pass-gueltigkeit.pdf

Just to elaborate a bit on what Sam, Jazz, and Chris F. advised about getting to Interlaken via the scenic Luzern route instead of the Bern route, in spite of it adding a few extra minutes--here's the difference in how much more scenic it is:
On the Zurich to Interlaken route via LUZERN, you'll pass loads of bright blue-green mountain lakes, mountains, and waterfalls down cliffs. From Luzern this is part of what is called the Golden Pass route, and it doesn't cost anything extra, and all the trains on this route have panorama windows.
On the slightly faster route to Interlaken via BERN, you'll pass lots of industrial centers, and I think what I spotted in the distance, the only time I went that way, was a nuclear power plant.

And the route via Luzern is actually cheaper, at least from Zurich. I think that is because SBB prices trains by the kilometer. The route though Bern is faster, because it goes over relatively flat terrain and does not make many stops so the trains go fast. The train from Luzern is narrow gauge, makes a lot of stops, and climbs over a high mountain pass with lots of tight turns, slowing it down. But it is the shorter route measured in kilometers.

I very much appreciate all the input that everyone has provided. Unfortunately, our time in Switzerland is short so we have decided to consider this an "excursion day" rather than a "means" to reach Interlaken. That being the case, we look forward to taking the longer, more scenic route via Luzern.

Do we need to advance train tickets in advance or just buy them at the train station after we land in Zurich? Also, I assume a rail pass does not make financial sense if this ride to Interlaken and a ride back to the Zurich airport (in order to fly home) will be our only train rides?

Also, do you think the weather the first week in April will permit some hiking in or around Gimmelwald/Murren?

Susan, if airport to Interlaken and Interlaken to airport are your only rail trips, just buy at the station. There is generally no discount for advance purchase, so no point in buying in advance on the internet. There are some discount tickets, but they require deciding on a train when you buy, not a good idea if you are flying in.
Except, will you be staying in Interlaken town the whole time? I doubt it, I guess you will be going further into the mountains (Mürren, Wengen, Grindelwald and up mountains), so you will have other rail and cable car trips.

All rail routes in Switzerland have at least one train per hour, so no need to worry about times, it is "turn-up-and-go".
You can look up detailed times and prices on the SBB (Swiss Fedral Railways) website: https://www.sbb.ch/en/
Times for next April are not yet listed, they will be 95% the same as current times.

"do you think the weather the first week in April will permit some hiking" - probably, hopefully.

Good to know the rail system is so efficient and operates on a quick pay as you go.

I'm still working on our 4 day itinerary (really 3 because the first day is flying to Switzerland and getting to Interlaken); however, we already have accommodations set in Gimmelwald. With such a short stay we don't want to venture too far, just take in the beauty all around us. We thought that we would explore Interlaken, Murren and go to the Shilthorn (closer & less expensive than Jungfrau and there are 4 of us), weather permitting. Maybe a hike or two. Any other must do/see in the surrounding area? Again, I can't thank you enough for all the recommendations and information.