Noob here. Overwhelmed by response to my 'for rent' sign.

[Lesley Futterknecht]

This is a good problem to have, but I have no idea what the best way is to handle it.  Hubs and I closed on our first ever income property last Friday.  It's an unoccupied duplex in a so-so part of town (but on the border of a good school district, which was part of the appeal.)  I was fully expecting it to take a couple of months to get tenanted.    We got the keys Friday, got the power turned on, and threw up a sign Sunday afternoon.   I've gotten easily 30 calls in the last 24 hours.  I'd say the property was undervalued, but the price isn't on the sign, just a phone #.   About half the people who called said thanks but no thanks when they heard the price, and the other half want to come see it.   DH and I both work, and he's out of town for the next few days anyway, so rather than making 15+ individual appointments, we decided to basically just open it up for a few hours Friday after work, and I've been telling people to come, have a look, and then fill out the application if they are interested, but I'm honestly totally blown away by the # of responses, and my phone is still ringing.  What should I do?  Keep telling people to come?  stop answering the phone?  Am I over thinking this?    

also, assuming we get applications from even half the people that are interested, any pointers on how to weed through them?   Income of 3x rent, no past evictions, stable employment, decent credit history?   anything else?  No smokers for sure (can I put that in the lease though?) and probably no pets.    Are families generally more stable/reliable than singles?  Or do you experienced landlords find that little kids tear up houses?    I don't want to choose the wrong tenant!