I don't see that anyone mentioned recorders here, which is odd since:
a) they are period to the renaissance
b) they are easy to learn
c) In the U.S., most school children learn to play one in elementary school, so many already have experience on them.
cheap wooden recorders can be bought at craft stores (like Jo-anns) for a period look - these are modern recorders based on the baroque instrument, not the earlier ren style, but get the job done for cheap if you don't want to invest in an expensive reproduction.

also, Music Makers (http://www.harpkit.com/) sells all kinds of reproduction instruments from the Middle Ages and Renaissance, including plucked psalteries, lutes, etc., and some hybrids catering to re-enacters that are basically guitars in the shape of a lute. I highly recommend them, my psaltery was purchased there and they have GREAT customer service.

I know this post is several years old and the OP is long past caring, but in case others in the future are looking... =)