Armadillo's or Kevlar Inserts?
Your sliding out at 5mph wasn't because the tires were slicks, it was for some other reason. They were either lousy tires, improperly installed, rider error, or some other factor.

If you are riding on the road, there is no need for any kind of tread. Slicks are perfectly fine, despite your thoughts from your previous experience. In fact, they are ideal, and will be easier to handle on the road than tires with tread. A definitely don't get any of those combination tread tires, those are the worst.

Forget the treaded tires with kevlar inserts. Get the Armadillos, Continental Gatorskins, or some other sort of flat resistant tire. Make sure they are always pumped up before you ride, and they'll serve you well.