To date I have bought nothing new to run commute. I have only repurposed other gear I already owned. I’m a single mother on a limited budget, and these are the things I use:
Backpack: Camelbak M.U.L.E. from which I have removed the bladder for run commuting. I have used this pack hiking with my children, trail running, and bike riding for years.
Raincover: This pack is weather-resistant, however this is the rain cover I intend to get… someday.
Hydration: Water or Gatorade G2
Jacket: Nike Run hoodie, so old they don’t make it any more.
Cleanup wipes: Target or CVS brand cleansing and make-up remover towelettes in the blue bag
Towel: Mission Enduracool Instant Cooling towel (also my camping towel) I wet one end and keep the other end dry.