So, wanting something that is good for on the go as well as home use. I prefer iem’s for on the go, if I want something bass heavy and efficient I like se846 or Atlas. For home use , I prefer open cans like Audeze LCD series or Senn 800s but they both need a boat load of power and u will need a new amp setup to get that deep clean bass, plus none of these headphones really fit in your budget.
So, my recommendation is the Campfire Cascade. Unbelievable low end, can use on the go, home and will be in that under 1000 range. Try to listen to the cans before you buy...but I’m telling you they are amazing for the parameters you have given....just google the reviews