Switzerland for 8 nights

8 nights - one in the city of arrival since you will be jet lagged, and one in the departure city. Flying into and out of Zurich which is much more central would make most sense to me, or arrive in one and depart from another. For the six intervening nights I would probably pick the scenic train route you want and pick the stops at either end of that. But, I would also include two nights in the Bernese Oberland (for me that would be Lauterbrunen (but others may have different opinions).

Have fun!

I think your list is a bit ambitious for 8 days. I think with your list of desires, if you can cut Zermatt/Matterhorn you can accomplish everything else.

Fly into Geneva (or Zurich if possible as it’s slightly closer). If flying into Geneva ride the Golden Pass Express scenic train (Montreux>Interlaken) and then stay up in Wengen for 4 nights to explore the Berner Oberland (Top of Europe/Jungfraujoch, Männlichen, First, Lauterbrunnen, Murren, Schilthorn, etc). Then train from Wengen to Luzern and stay there 4 nights. From here you can do a day trip to Bern as well. Then train directly to the Zurich airport from Luzern (1 hour).

Landing at Geneva, it would make sense to spend 2 nights in Montreux to break the journey to the Berner Oberland. It is a beautiful area.
So, 2 nights Montreux, 3 nights Berner Oberland, 3 nights Lucerne, or 2-4-3.

Or, if you absolutely must try to see the Matterhorn, replace Montreux with Zermatt - but travel time is much longer, you miss the lovely Golden Pass railway, and Zermatt just isn't that great if the weather does not cooperate.

Zürich airport is easily reached from Lucerne as long as your flight is not super early.

Would it be a good idea to just do a base city and do day trips?

Yes. With only eight nights, you don't want to lose time relocating. As to which city, that will depend on the day trips you want to do from your base.