Any tips for traveling around and being more portable with a dslr? You tend to hear people loving to take photos with a phone just because it's easy to carry around and it's always on you. What are people doing to make it easy to carry around their camera and quickly snap photos?

I'm using a D5100 with an SB-700 flash. I have an over should strap but it's not perfect. It's easy for the camera to tumble around, clip people, etc when you're just trying to get from point a to point b. Add an SB-700 flash to that and it's even more cumbersome and unwieldy at your side. Then I'm also fumbling around with the lens cap. If I'm moving through a crowd I kind of want it on to prevent finger prints, water drops, whatever but it's an extra step to remove when I want to just quickly get a candid shot.

Along these same lines, instead of gear, what kind of shooting settings do people like to fall back on for quick shooting like I'm describing? I prefer aperture priority mode. Recently found out I could set my D5100 to limit the shutter speed to a minimum of 1/100, at which point it'll up the ISO to a point to get the correct exposure. Really enjoying that, but curious what others do.

EDIT: Does a mirrorless like the Sony a7000 or Nikon Z6 or whatever make this any easier? Not that I'm in a position to drop a significant amount of money, just curious (got my D5100 used for $200 a couple years ago and jumped on the SB-700 for $100 used if that's any indication of my price threshold).