Which train company from Geneva to Luzern?

The only national Swiss rail line is SBB. You are looking at third party ticket sellers. Download the SBB app. Purchase tickets directly from SBB.
Have a great trip.

Thanks so much!

Thetrainline and Raileurope are TRAVEL AGENTS. They only sell tickets for somebody else's railroad.

But to your question, the "Golden Pass" scenic route takes 6 hours, whereas the lowland route takes 3 hours.

Thanks! You can tell we’re newbies to this! 😉

Trains in Switzerland are mass transit. Taking the train from GVA to Luzern is pretty trivial. Upon arrival at the GVA airport you just go to the railway station at the airport, buy a ticket and travel. If the whole prospect of railway travel is now to you maybe that is what you should do. Just go to the ticket office and let one of the friendly SBB agents help you.

You can purchase tickets in advance to save you having to deal with the ticket vending machine upon arrival, but do pay attention when doing so: SBB nowadays sells two kinds of tickets. Normal tickets ("Point to point") are good for any train on the route they have been bought for, for a whole day, and thus allow you to take the first convenient train to your destination once you are out of the airport, not just the one you selected during purchase.
But they also sell supersaver tickets, which are cheaper, but which are not flexible. With these tickets you need to take the train you selected during booking and if you miss that, you just forfeited your ticket. So think about that when buying tickets.

What are your plans in Switzerland? If you plan on doing more trips (especially mountain trips) some pass may be useful for you.

Wow - that’s super helpful - thanks. We’re taking the Rick Steves 12 day Switzerland tour and then going from Bern to Geneva to spend a couple more days. We haven’t planned everything out for sure yet, but I think the only other train we would need is the Bern to Geneva. At what point do you think it would make sense to buy some sort of pass?

We are flying into and out of Geneva, but we need to get to Luzern
where our tour starts. It looks like there are at least two options
(thetrainline and raileurope) plus possibly some scenic routes. A
scenic route would be great if it doesn't take too much longer than
the 3 hours on the main lines. Any recommendations?

As has already been pointed out these are agents not different Swiss companies. And while we do indeed have different rail companies in Switzerland it is for administration and subvention purpose, so it makes no difference to the travelling public which company runs a particular train - all times and fares can be found on the sbb.ch website.

The Swiss rail companies have different liveries, differences in carriage design, luggage space, bicycle space and so on. So it would be useful to know which company was running a particular service if you were bringing a bicycle or over sized luggage for instance.

Or if you'd rather, the all-knowing Man in Seat 61 lists travel agencies in Europe that do trains