You need to get a book, because there's lots to know about the dulcimer. There are different ways to tune it and to finger it. As a result, it can play a remarkable variety of sounds.

In my opinion, the most productive way to tune is D-A-A. Read a book and you will see why. Examples of D-A-A songs:

Down by the Salley Gardens
Praise to the Lord
Morning has broken
Salve Regina
For the beauty of the earth


When I am bored with that, I use D-A-G. Tuning D-A-G requires that the fingers go on different frets to get harmony. I use stickers such as children play with to mark the positions for the D-A-G chords.
Examples:

God rest ye merry, gentlemen
Black is the color of my true love's hair
The great silkie
Let all mortal flesh keep silence
Banks and braes of bonnie Doon (or is it Doone?)

I wish I lived near you, then we could get together.