>> ... and have never taken Switzerland's trains, so I'm a little anxious about it, especially given all the connections required to get to Lauterbrunnen.
Time and time again, first-time travellers to Switzerland mention how easy it is to travel by train, and I’m sure you will be no different :-)
Regardless of which route you choose, you will be able to transfer between platforms or out onto the street without encountering any steps. Most stations will have a ramp, and some also have lifts and/or escalators. At some stations, the platforms, concourse and street are all on one level, and you don’t even need to use a ramp (e.g. Luzern). Sometimes your transfer could just be from one side of the platform to the other. The timetable will tell you in most cases on which platform your train will arrive, and from which platform your connecting train will depart. Platforms are well marked and signposted.
>> If given a choice, would you say the trip from Zurich Airport, or Geneva Airport, is easier to navigate by train? … I must fly out of Geneva on my outbound flight.
None of the options are the least bit difficult, so my suggestion is to pick the most scenic options :-)
If I were you, I would fly into Zürich and out of Geneva, and incorporate the Golden Pass scenic route into both your incoming and outgoing journeys.
Zürich Airport to Lauterbrunnen
From Zürich Airport, travel to Lauterbrunnen via Luzern. The sector between Luzern and Interlaken Ost is particularly scenic, and forms part of the Golden Pass route. You will change trains at Luzern and Interlaken Ost before arriving at Lauterbrunnen.
Luzern is a very easy change, most likely from Platform 4 or 6 to Platform 12, all on the same level, so no stairs or ramps. You will be able to roll your luggage onto the train at Luzern, as at least some doorways of the train are level with the platform (look for the wheelchair graphic on doors). Sit on the right for the best views.
Then at Interlaken Ost you will need to change again. This applies regardless of which route you choose. You will be able to roll your luggage off the train at Interlaken Ost, and transfer to your next platform via ramps.
At Interlaken Ost, you will board your next train on Platform 2. The timetable will tell you that your train to Lauterbrunnen departs from Platform 2A. (If you were going to Grindelwald, it would tell you that your train is departing from Platform 2B.) It is all the same train, but the carriages will be split at Zweilütschinen. The carriages that started out on Sector A of Platform 2 at Interlaken Ost will continue to Lauterbrunnen. Those that started out on Sector B of Platform 2 at Interlaken Ost will continue to Grindelwald. It is very easy to find the right section of the train, as the platform sectors are shown on blue-and-white signs above each platform. You can also double-check the destination as you board the train, as it is displayed on the side of the carriages near the entrance doors.
Lauterbrunnen to Geneva
You can travel from Lauterbrunnen to Geneva by incorporating the Golden Pass route from Interlaken Ost to Montreux via Zweisimmen, then get normal trains to Geneva. This takes longer, but is by far more scenic than going via Bern.
Depending on the connections you choose, you may need to change trains at Spiez. This is a very easy change on the same platform – either Platform 2 (the same side you arrive on) or Platform 3 (the other side of the same platform).
At Montreux, it will usually be a platform change from platform 6 to platform 1. There are escalators and lifts in Sector B of the platforms.
It would be a good idea to reserve seats for the sector Zweisimmen to Montreux, as this can get busy with large tour groups.
There is more information about the Golden Pass route here: