An interesting question and  not an easy answer.

Reservations split into 3 types. mandatory, optional and not available. 

The first and last of these are simple, but optional reservations are the challenge.

We have just finished 2 trips using a first class 10 days in 2 months pass, but there were only 2 of us so fees were not too bad. Most of our journeys had mandatory reservations (Italy, France and Eurostar) and we took optional reservations in Germany (ICE) and the UK when they were likely to be busy. That paid dividends as two of the trains were overfull - optional reservation trains allow standing so you are unlikely to be left behind (but it can happen).

Mandatory reservation trains only sell to match available seats.

Given the full holiday budget (pass, accommodation and spending money) this extra was insignificant.

On the many regional trains without reservations that we took there was no problem other than occasional peak time commuting trains, much as you get at home. 

Always have a plan B (and C).

Always make a reservation in the UK - they are free for most routes. I assume you have your Eurostar bookings.

With 6 people you may want to book seats so you know you'll sit together. However, without knowing the exact trains (route, date and departure time for each train), it's not possible to give much advice on whether they're recommended or not. I'll just say that in Swiss domestic trains, you don't need reservations (although they're possible).