I couldn't bear to glue anything to the *beautiful* book-matched walnut on the back of my newer dulcimer, so have a guitar strap on mine (we jokingly call it a "seatbelt"). Other people cut up pieces of non-skid rug liners and to put between their thighs and the dulcimer.
I learned first in DAA but quickly switched to DAD because, especially if you intend to play with other instruments, it's more versatile. Another thing I did, although this approach is disputed, is I'd play a tab through a few times on just the melody string, to get the hang of it, and then I'd go ahead and try to play it with the chords before I got too used to playing on the melody string alone. It takes a lot longer to learn tunes this way, especially if you're just starting out, but I think it kept me from becoming "afraid" of the chords and ultimately made me more comfortable with the instrument, and a better player.