Hi Curlgagan- Good time to visit. Definitely into "summer" season, but the real crowds are not really there yet. Likely still plenty of wildflowers in the alpine meadows
Those are popular routes, but they have frequent train service. You'll likely go from Zürich to Bern, change trains, and go to Interlaken Ost. The train from Zürich probably does not originate there, but there are usually major numbers of passengers disembarking and embarking, which frees up seats ...especially if you are the first ones on. Zürich is a terminal station. The tracks dead-end.
Bern ( where the train most likely also comes in from somewhere else) is a "through" station. If you are trying to make a tight connection, you'll want to be somewhere near the middle of the train going into Bern. That will place you close to the inter-track passenger tunnel. However, the cars with fewest passengers tend to be at the end furthest from the rail head in Zürich.
One way to get an idea of how crowded the trains are is to check the time table. The time table gives clues about how busy the trains are (note symbols for predicted occupancy, which will vary during the day) the inbound and out-bound track numbers ( sometimes all you have to do is cross one platform....) and connection times.
I have attached a couple of screen grabs.
I picked the slowest route, which has less predicted occupancy. You change at Bern, but also at Spiez.
Here is a map of Spiez station.
www.sbb.ch/content/dam /infrastruktur/trafima ge/bahnhofplaene/plan-spiez-a4.pdf#?lang=en
At Spiez, you have a three minute connection, but tracks 2 and 3 are on two sides of the same platform.
At Bern, you have a six minute connection, tracks 5 and 6. They are on the same platform.
Other trains on that day or other days may use different platforms, but the SBB tries to keep major route connections on one platform, when it can.
if you miss a connection, you will have another one in half an hour or less.
If this is your first trip on the Swiss trains, or if you are going to be let-lagged, I'll change my comments and agree that reservations would make sense for a party of 6 on the route you have given. These are high occupancy routes. You will be able to get seats without reservations, but, it may be difficult to stay together. First Class is better, with lower occupancy, and more comfortable seats, but adds significant cost, and second class is quite acceptable.
<<"Can we wait until we arrive in Switzerland to make reservations? How far before train departure must you make reservations? One week, one day, one hour?">>
I must confess that in 35 years of traveling by train in Switzerland, with parties of up to four people, I have never made reservations. The exception - traveling on international trains to Italy, Austria, or Germany, since they are required once you leave Switzerland. So, i don't know the answer about how far ahead to purchase. Arno and Annika (forum moderators) are more likely to have that answer.
Sorry for the long answer "non-answer." ;-( Perhaps the information on using the timetables and station maps can be useful. And, with experience on the trains, you may find that you do not need reservations on later segments.