Swiss Travel Pass - 1st or 2nd class

Easy answer. 2nd class is perfectly fine.

Seconded, second class is perfectly adequate. Second class has 2+2 seating, first class has 2+1 and proportionally more legroom. That is the only difference.
An 8-day Swiss Travel pass costs CHF 363 2nd class or CHF 581 1st class. I don't know where you come from so I don't know what type of '$' you are talking about. Details here: http://www.sbb.ch/en/leisure-holidays/holidays--short-breaks-in-switzerland/swisstravelsystem/swiss-travel-pass.html
You will need to buy two passes for the two adults and a (free) Swiss Family Card. Children under the age of 16 travel free of charge when accompanied by at least one parent holding the Swiss Family Card.

How many days of the 7 will you actually be travelling? At least 3 (Varenna to Lauterbrunnen, Lauterbrunnen to Luzern and Luzern to Salzburg), but will there be any more? It may be cheaper to get a Swiss Travel Pass Flex (3 days in 1 month for CHF 239 2nd class or CHF 382 1st class). Or it may even be cheaper to buy a Swiss half price card and half price tickets. You will have to do some arithmetic yourself to work this out. And don't forget, Swiss passes of any kind only cover travel within Switzerland, you still need to buy tickets from Varenna to the Swiss border and from the border to Salzburg.

Thanks sounds like 2nd class it is. My prices were a total price in USD for 2 adults and 2 kids.

My thought with the 8 day is that we will be doing some train rides while in Lauterbrunnen and Lucerne, plus it sounded like the Swiss Travel Pass can get you entrance to certain tourist venues, but maybe I'm not right about those things and three day will be fine for us.

Yes, the Swiss Pass also acts as a museum pass. But are you going to see enough of these to make it worthwhile for your family?

To get the list, go to this page. Near the bottom you'll see a red arrow next to "To the complete list"; clicking on that will open a PDF listing all the museums covered. http://www.swisstravelsystem.com/en/rechtliche-hinweise-swiss-pass.html

Thank you for all the great feedback. I priced the journey and it turns out it will be quite a bit less expensive to buy the tickets without a Swiss Travel Pass or Half Fare Card. The reason is that the Varenna to Swiss border and Swiss border to Salzburg legs are a big part of the overall cost. In any event, the three legs Varenna to Lauterbrunnen, Lauterbrunnen to Lucerne, and Lucerne to Salzburg are not all in all that expensive, which was good news. Part of the reason is the kids seem to be able to travel free on the Lucerne to Salzburg leg. I priced everything at www.sbb.ch. I hope I did it correctly! :)

Now I'm wondering do I buy the tickets now or wait until I am in Europe? Do they do e-tickets or paper tickets?

In Switzerland, it is not necessary to buy advance tickets. But in some cases, you can buy Supersaver tickets up to 30 days in advance. For instance, Lauterbrunnen to Luzern can be done for 23.80 CHF vs 39.80 CHF regular fare. You will have to pick the exact train you want and the tickets are not valid on any other trains.
http://www.sbb.ch/en/travelcards-and-tickets/tickets-for-switzerland/supersaver-tickets.html

Rdavidorf - your kids will travel free with you everywhere within the Swiss Border. Just get the FREE Swiss Family Card when you buy your pass. If you're spending time in the Lauterbrunnen Valley area and are taking a trip to the super expensive Jungfrau (which you DEFINITELY should do) you should invest in a Half Fare Card. The savings afforded to you from that 1 trip to the Jungfrau will almost pay for Half Fare Card. I say you should definitely go the Jungfrau because your 2 sons will travel with you for absolutely free. That's a great deal!