<<"My dates are June 30 - July 10 so I have 10 nights. Would this help in answering the questions?">>
You have picked good dates. Probably will see a lot of wildflowers...June is a good month for that.
The heaviest tourist traffic is in August. You are going to be there just before it starts to pick up in July.
If you had said early June, I would have had to caution about many closed services and facilities. because the higher altitudes usually have snow blocking trails and roads. About June 15th is when "Summer" season begins.
in mind as you plan, in addition to going through the information in the link I posted above about he Bernese Oberland. That earlier link will help you choose a base or perhaps two in the B.O.
<<"Should we stay for 1 or 2 nights in Zurich and then head to Lucerne? Stay the night in Lucerne?">>
Unless you arrive very late in the evening, I'd go right to Luzern. A train twice per hour takes one hour. Based on your stated goals, you could even skip Luzern and go right to Interlaken or one of the towns south of there, but you have enough time that a day or two in Luzern will still leave lots of time for the B.O.
One train from the airport to Luzern each hour goes direct with a stop in Zürich, the other requires a change in Zürich. See the timetable I linked above. If you wish to stop over to walk around Zürich a bit, there are luggage lockers and a a more expensive left luggage office.
Luzern is close enough that you can use Zürich airport as the airport for Luzern.
The remaining questions involve subjective and personal judgements. You really have to answer them yourself, after studying the links about the B.O. as well as Zermatt, Zürich, and Luzern on the page:
Luzern is rewarding to the first time traveler, with a great variety of things to see and do. Zürich is rich in culture and other items that are best enjoyed on a longer stay after you get to know the city, but a walk around the old town on both sides of the river is enjoyable. The Lindenhof has some pleasant and interesting views.
Do you have special interests? Are you a hiker or do you hope to do some walking on scenic trails? Museums? Luzern has all of those easily accessible.
<<"- Would you recommend the Golden pass line to Bernese Oberland?">>
If you are staying in Luzern, that is the best way top go to the B.O. Quite scenic. The other reasonable route goes through Bern. Bern should be left for a contingency plan for bad weather in the B.O. or if you have seen enough of the B. O. area.
<<"- Where should we base ourselves from? Interlaken? Grindelwald? Gstaad? How many days should I spend in the Bernese Oberland? Spend a couple of nights each?">>
There is good reason to pick just one, or at most two bases in the B.O.
For access to the "outside world" Interlaken is better, ( saves time) but it is not all that scenic or as enjoyable as Lauterbrunnen, Wengen, Mürren, or Grindelwald. Each of those has different character; read the link on the B.O. posted earlier. All of those meet your goals. Look at the map and the time table.
www.swissholidayco.com /Public/Assets/User/fi les/Map-of-Jungfrauregion1.jpg
I like Wengen. Here is a little useful information from an expert:
<- Does one stay at the base and then just make day trips or stay for 1 or 2 nights across these places?">>
See above comment.
<<"- Should I also try and add Zematt?">>
That is up to you. It is spelled Zermatt. The Jungfrau region has enough to fill all of your time, especially if you are a walker,
www.jungfrau.ch/en/som mer/tourism/destinatio ns/kleine-scheidegg/hiking-trails/
but the train ride to Zermatt is very scenic and historic, if you pick the old route via Spiez to Brig and onward to Zermatt via Kandersteg. The special train is called the Lötschberger and is definitely worth riding while you are there, even if all you do is go to Brig and return. Sit on the right going toward Brig.
If you are serious about walking, there is an interesting "Rail Trail" that parallels the train as it descends the wall of the Rhone Valley toward Brig.
Zermatt is smaller, but is the favorite of many people. Annika knows it well and likes it.
See the link on the "Where to Go" page linked above.
Check the timetable, and choose Kandersteg as a "via"in order to force it to the slower route and avoid the faster new boring "basis" tunnel.