First off, You are going to get 10,000 opinions with this question. Forget the prime crap. A true walk around lens will be a zoom. An 18-300mm would be great. There are some lightweight ones out there. Just use google and also go to the Nikon site. See what they have to offer vs. your budget. Also, do not worry about the lowest aperture. A 3.5 or a 4.5 is just fine even in low light for the average photograph. Nothing wrong with an 18-250mm lens either. You are going to want more than an 80mm maximum reach.

Walk around means that you will be shooting anything from closeups of bees to a bird way out there. This also includes average people shots, obliques of a cool looking automobile, even portraiture and landscapes. If you know what you are doing, you can even do nighttime shots without too much trouble and a lot of excessive gear.

I will give you a good example: I am using an average, run of the mill Sigma 18-250mm F4.3 lens as my walk around. I only paid a couple of hundred bucks for it. I shoot anything and everything with and without flash. Do you want to see how well it works? Just check out my last 100 posts or so on UHH. My posts run the full gamut. I have portraiture, critters, flowers, people photography, kids birthday parties indoors and out. Also included are festivals, fairs, landscapes, birds buried in trees, you name it. I even have low light posts shot without flash that I brought up in post with no noticeable noise. And this, all done with a crop sensor. On your D500, you will do much better, especially in low light conditions. I have no problems with chromatic aberration either. Sometimes I may have a little distortion here and there, but all lenses will do that under certain settings and conditions. No big deal. I also have a 70-300mm lens that does a super job, but I like the 18-250 better because I can use it close in such as indoors in small rooms.

So, do your homework starting out by looking at my stupid posts, use google, and the Nikon site as I have mentioned. Look and see if there is a Sigma or Tamron that will fit you needs if budget is a problem. If you have the money, Check out the Nikkor lenses. They are excellent and they don't way a ton either.