"The Mosel is best done by car. "
The Mosel, along with Trier and Luxembourg, is a somewhat roundabout way of getting to Liege. Perhaps you would visit the Mosel on a day trip from Koblenz during your stay there?
"Best" is pretty subjective. It's not clear to me whether your current plans include sightseeing along the Mosel, and if they do, then how many days you might have to explore the river towns. But let's say you have wisely included the Mosel in your plans in some way...
If "best" for you means following the entire Mosel riverbank route on its very windy 200 km meander from Koblenz to Trier, then you must do this by car, and you must plan for a lot of time in your car. Keep in mind that you won't be driving through all the towns since there are two river banks. The road switches riverbanks here and there but you'd have to double back to hit them all.
OTOH if you will visit the "highlight" towns - Cochem, Trier, Traben-Trarbach for example - a scenic train trip will get you to most of them quickly and easily. (Bernkastel involves a train ride to Wittlich + a bus connection.) Just as you can by car, you can follow the riverbank from Koblenz to Cochem (about half the distance to Trier as the crow flies) by train as well. This downstream half of the Mosel is not nearly as windy as the upstream half - so the 1878 Mosel Railway construction project found it easy to build right along the river; just like the road, the train follows the river for every km on its way to Cochem. The scenery will look much like this for the whole trip. There are 14 station stops from Koblenz to Cochem - see this train line map of the Mosel route. On a day trip by train you might want to stop off for an hour or two for a meal and a walk around town (train service is hourly or better) in Winningen or some other town.
After Cochem, the train heads through a long tunnel - then continues along the river past Neef to Bullay. (The train takes only about 9 minutes to get to the town of Bullay, vs. about 40 minutes driving.) After Bullay, the railway leaves the river almost entirely on its way to Trier.
The "best" way to enjoy the Mosel River itself is on a cruise boat, IMHO. There are several boats per day between Cochem and the small town of Beilstein (a 1-hr. cruise.) So a nice day trip option from Koblenz is 1.) train to Cochem for sightseeing, 2.) river cruise to Beilstein, 3.) return train to Koblenz. Another fine (and longer) cruise is the one between Traben-Trarbach and Bernkastel.
Another popular day trip: 1.) train from Koblenz to Moselkern, 2.) walk from Moselkern to Burg Eltz and back 3.) train to Cochem for sightseeing, 4.) train back to Koblenz