Shipping from Amazon, by UPS--when?

I’m not big on online purchases, so with this recent purchase I made from Amazon I am not sure what to expect delivery-wise. I’ve been tracking the package and now it’s in my town, “out for delivery” since early morning. It cost less than $50 and should be about backpack-sized. I used Amazon’s free delivery thing. So my question is, should I sit and wait by the door because they will just leave if I don’t sign, or can I go out and come back and expect it to be sitting at my doorstep? And also, after the package is “out for delivery” in my town, how long should it take for it to come to my apartment? Amazon’s estimate still says to expect it on September 4, but I can’t imagine that it would take two weeks to deliver it in a tiny town like mine.