Lake Como to Basel

Milan for Como, certainly. From there you can organize your train route Como -> Basel using Rome2Rio (an app that gives you all transport options for whatever route and date you enter, including schedules for those transport options)

Milan MXP for Lake Como. Take train via Zurich to Basel.
Are you driving or taking trains? You don’t want to return a rental car to a different country, very high drop off fees. Train should take a little less than four hours. Do you want to go directly to Basel or only get there to depart? Where do you want to stop en route?
Highlights in Switzerland are the Betner Oberland. Stay in Grindelwald or Wengen.
Also near St-Moritz, stay in Pontresina. These are charming towns with big views of the Alps!!

Thank for the tip on Airport. Any recommendations for sights/towns between Como and Basel?

If you fly into Milan, you’ll need to take a direct train from the airport to the Milano Centrale station (45m). You can sleep in Milan and take a day trip to Varenna and Bellagio that’s doable or you can continue on to the Varenna-Esino train station (1h 15m) and sleep on Lake Como.
To get from Varenna to Basel you need to transfer at the Milano Centrale station. There is a left luggage area for you to store your bags. There are a couple direct trains from Milano Centrale to Basel (5h) so if you stop along the way make it Milan.

If you want to see sights in Switzerland, you might want to stay in Varenna on Lake Como. Then train to Tirano then train to Chur. This is the Bernina Express route, although you can take regular trains without the reservation fee. From Chur you can get to Basel by way of Zurich.

Taking a direct (no transfers required) train from Varenna to Tirano takes 1h 30m and a train from Tirano to Chur takes 4h 15m with two connections taking a total of 5h 45m; this route will be more scenic. I don’t know but be prepared (means pack light) if there are stairs at any of these stations where you have to haul luggage up and down steps to get to platforms.

There are also direct trains from Chur to Basel but not many (2h 30m).

then will be flying out of Basel

To where? If it is back home, that is a bad idea in my opinion. Basel has a small airport with very limited options.

Thanks everyone! We are definitely now flying into Milan on Saturday, staying around Lake Como for one or two nights. Then taking a/multiple trains toward Basel (we will not fly out of Basel after all but continue on to France). Arriving in Basel on Wednesday. We're thinking Lugano, Andermatt, Luzern for the remaining two +/- days/nights before Basel. Do you believe we have time for these places with our travel plan? Do you think the Bernese Oberland or the SBB or both would be our best bet for train travel?

Do you think the Bernese Oberland or the SBB or both would be our best
bet for train travel?

The Swiss federal railways, SBB/CFF/FFS, runs trains. Berner Oberland is a region.

With the pent-up demand for European travel this summer, many posters have reported lodgings already being fully booked. I'd suggest you draft an itinerary soon and quickly look into lodging options. That could affect where you're staying.
Safe travels!