The Mosel Valley is a well-known wine region but you can certainly find beer there. Since you are using public transport, the choice of a base town for the German Mosel should be informed by the actual transportation options there. I'm posting 3 maps for you below.
Here's a map of the main train line there, the Trier - Koblenz Railway. (Only the more important stations are shown - there are many other stations as well - so use this map to pin down all the smaller stations. Only the towns on the dotted railway line have stations.)
You might not even notice it on the main train line map, but there's a small gray squiggle that heads south from the main line at Bullay. That's the Bullay - Traben-Trarbach Railway, and here's an expanded view of that route, also known as the Mosel Wine Railway (Moselweinbahn.)
Obviously, you'd be best off with a town that has a train station, a town that is central to other Mosel destinations.
Cochem is one such base town, probably the most popular of the choices. From there you are a short distance to Burg Eltz Castle and within day-trip striking distance of Traben-Trarbach and Trier by train. Bernkastel is a fabulous old-world destination as well - and from Cochem it's easy to get there; just take the train to WITTLICH (which is mostly forgettable) and transfer there for the bus ride to Bernkastel. RJean has mentioned Beilstein - also a popular destination. Beilstein has no train station - not a good base town choice - but if you are staying in Cochem for your outings, you can easily catch a river cruise boat to Beilstein and be there in about an hour.
Bullay is another good base town option. Choose Bullay if you want to be somewhere non-touristy and quiet (and probably a little less expensive.) Bullay is considerably smaller than Cochem - but less than 10 minutes from Cochem by train. Obviously, getting from Bullay to Trier, Bernkastel (via Wittlich, as before), and Traben-Trarbach will require slightly less train travel time. (Note that for Bernkastel, you could take the train to Traben Trarbach and the river cruise from there to Bernkastel. A very nice trip!) Want to take the river cruise from Bullay to Beilstein? That's possible too in about 1.5 hours.
I am no doubt one of the few forum members who has stayed in Bullay (3 different occasions.) Most accommodations there are vacation rental apartments, and there are just a handful of places to eat. It's a very nice spot for doing bike rides along the river (to Zell for example, very close) or walks/hikes to scenic outlooks (Marienburg, or Burg Arras Castle.)
I have stayed in Cochem several times as well. Cochem is far more touristy and busy with daytime crowds. But it's still very precious.
After your Cochem or Bullay stay... I suggest you travel to Luxembourg for 1-2 nights. Instead of doing a day trip from Cochem to Trier, what you could do is a STOPOVER in Trier on your way to Luxembourg. Just park your bags in a station locker and see the town for several hours, then head to Luxembourg in the evening.