Train Pass Confusion for Switzerland

A lot depends on your "day trip" plans, since the lifts (Schilthorn, Jungfrau) are expensive and need to be considered when comparing costs of pass/ half-fare card/ point-to-point.

I agree with Laura, it is not the trips you list, but the ones you don't. How are you getting from Lauterbrunnen to Winterthur?
And what comes before Basel? Are you buying a through ticket from XXX to Basel, which may be cheaper than separate tickets XXX to Basel and Basel to Lauterbrunnen?
Consider either:
1) Separate tickets (unlikely to be the best option as you will almost certainly be doing extra trips, e.g. up mountains).
2) Swiss Pass, gives reductions on day trips mountain trips.
3) Berner Oberland Pass ( http://www.regiopass-berneroberland.ch/home-en ). Better coverage of mountain trips, but still requires tickets from Basel and to Winterthur.

You will need to list out ALL your planned trips, and do some serious arithmetic.

Thank you so much.
We will be arriving by plane to Basel BSL Apr. 29
Train direct? from Basek SBB to Lauterbrunnen
Mountain train rides for at least two days May 2 & 3
We have friends touring us for two days in the Zurich area and will drop us at the Winterhur Station May 6
May 6 directly from Winterhur to Chiasso

macsppi, Thanks for the extra info. So you are getting free transport from Lauterbrunnen to Winterthur (note two 't's), that explains the gap.
It is not a direct train from Basel to Lauterbrunnen, you always have to change at Interlaken Ost. But that is not an issue. One train comes in and the other is sitting waiting. Swiss efficiency. The only catch is the train divides en route. Make sure you are sitting in the half going to Lauterbrunnen - signs on the sides of the vehicles and on the platform.

As you will be getting lifts, you are the exception to the rule and the best option is just to buy full-price tickets Basel - Lauterbrunnen and Winterthur to Chiasso.
From Basel airport there is a shuttle bus to Basel SBB station. There is an SBB sales counter in arrivals, and you can buy a ticket from here to anywhere in Switzerland, which includes the airport bus. There is no advance discounts or reservations on Swiss trains, so don't worry about that. Just go to aforementioned SBB sales counter at the airport, they will sell you the ticket and tell you the times of the next connections and even the platform numbers.

Normally it is a good deal to get the Berner Oberland Pass as it gives discounts on the mountain railways (details here: http://www.regiopass-berneroberland.ch/home-en ). But, the shortest period is CHF 250.- for 4 days. If you are only going to be there for two days it may be cheaper just to get full price tickets.

We are so thankful for the information received. Our trip has been simplified and now we will be planning the second portion in Italy.
We may require assistance in the future but want to thank everyone and the Rick Steeve site.