The first thing that comes to mind here: were you hired to serenade the visitors?

Rennfairs vary considerably in what they encourage/discourage and how "in period" they expect anything about the place to be. Unless you've specific information otherwise, don't be surprised if the fair management doesn't encourage free lance musicians, particularly ones who just acquired their instruments. Most tend to have scheduled (paid) musical performers & even those who appear as "buskers" are staff people with a schedule.

If you know how to play a recorder, that's an easy thing to carry with you, not as likely to get damaged, and easy enough to hang a small sack from your belt. If this is your first fair, just leave the musical toys at home and go have fun.

HOWEVER - if you want an early music instrument with strings, you've got a good electronic tuner, and money to spend... I HIGHLY endorse the bowed psaltry. Once tuned, it's dead easy to play. I shun the insults of "a fiddle for autoharp players" (I'm quite decent on autoharp, thankewverymuch) I've seen embroidered & woven pieces dated to the 1600s that show instruments like a bowed psaltry being played. It is an instrument folks either love or hate, & tends to carry over a distance. I've seen psaltries (and harps and other instruments) of various qualities on sale AT the fairs.

I have to surpress a desire to guffaw roundly at the idea of "in period" for some of the fairs I've attended the "period" in question would have to be "fantasy novels published in the last 100 years." At the "Medieval fest" closest to me, some SCA friends and I have snorked at "turkey leggs" and tacos at the food stand, fairy wings tied on the back of large ladies and grumpy rottweilers, numerous guitars & "Amazing Grace" on the bagpipes. At a (mostly) more historically accurate one downstate we were enchanted, in a most unperiod fashion, by a man who played glass'armonica of different sized glasses filled with water, and we waltzed to "Ashokan Farewell."

Just go have fun,eh?