The best amplified acoustic sound you will get is from a good mic and a PA. A guitar amp is designed primarily for a magnetic pickup. This will give your dulcimer an electric guitar sound. If this is the sound you want, that's what you do to get it. If you want an amplified sound as close as possible to the acoustic sound of your dulcimer, a good mic and PA is the best way to go. The problem here is the expense can be more than some of us want to spend, for casual gigs. Somewhere in the $600 and up range for the PA, and at least $100 for the mic. Add ons such as equalizers or pre amps may send it up a good bit more. And studio quality mics are delicate things no one wants to use in a live situation where travel is involved. These mics can run to as much as several thousand dollars each. Large studios use them, they put them away after the session is finished. There are guitar amps designed with the idea of amplifying acoustic guitars, and these can be a good compromise instead of a PA. Most have 2 to 4 inputs, probably not more. Mine will take a guitar or a bass, and a vocal mic. I have run it with a guitar, bass and a mic, but it isn't really intended for a multi-instrument set up. The PA is the better choice if you want to plug multiple players and vocal mics into it. Unless everyone brings their own amp.
Mics are made with different pick up patterns, as Robin said above. Uni directional mics are semi deaf in certain directions. This keeps the clacking of the pool table in the audience from being as loud as the dulcimer-or louder! It also keeps your sound your, not the player next to you. An omni directional mic will pick up in all directions. I have a couple that pick up every conversation in a coffee shop. In a place where not everyone in the audience is there for the music, this can be a problem. And crowd sounds, especially clapping, can be deafening. We point the mic at the singer or instrument, and turn the deaf side towards the crowd. For recording a large group such as a choir with one mic, an omni may be better, but choirs are seldom booked into coffee shops and bars. A concert hall is generally a quieter place.
Paul