We are a family of 4 looking at going from Lisbon to Porto in late March via train, bus, or private transfer. We prefer to include a stop in a town in between for a few hours if possible. If we are to take the train/bus is there luggage storage near the Coimbra train station? If we want to hire a driver, which company can you recommend, and is it worthwhile to visit another town on the way or is Coimbra the best option?
Coimbra is a great option, and there are lots of other great options, so it's not possible to say Coimbra is the best option. Think about how early you can get going out of Porto and how late you're okay arriving in Lisbon. Work out the timings to determine how much time you'll have in Coimbra.
There are lockers at Coimbra-B train station, and there is also a service called Nannybag (https://www.nannybag.com/en/luggage-storage?small=1).
Note that Coimbra-B (the main train station) is not in the center. There is a free shuttlebus from the train station to the center. It runs frequently. I had no trouble at all when I visited last year finding the bus stop at either end.
Also, be aware that getting to the university (which is one of the top things to see i Coimbra) from the center is uphill all the way.
I did Coimbra as a day trip from Porto, as it's much closer to Porto than to Lisbon. On my way to Lisbon, I stopped and spent the night in Tomar, which I loved.
Well, I loved Lisbon, Porto and Coimbra. We took a Bolt ride share from the train station to the university.
Do reserve a time to see the library at Coimbra the second you buy tickets at the university. I thought it was spectacular.
If your family includes teens or tweens or younger kids, I especially recommend the sardine cannery tour! A subway ride from Porto. The cork museum on the other side of the Douro held my interest. And the 45-55 minute boat ride on the Douro was excellent.
In Lisbon, in my opinion, the tile museum and Belem should not be missed.
All three destinations have hills.