Unfortunately, renting a parking space almost never includes the right to sleep in that parking space (unless it's at a campground), so you'll still usually get kicked out once discovered. You are an increased liability for the lot owner, so they and their insurance company and lawyers really don't want you there. It is also likely against local laws, zoning regulations, or other rules.
If you are lucky enough to find a paid parking spot in a place where it is legal, the owner has the proper insurance and permits, then follow the best practices for free parking in business lots. If you have a low clearance vehicle, the best paid spots may be in parking garages since they are sheltered.
You will almost certainly never be allowed to camp or sleep in a storage unit, even if your vehicle fits inside. They are not designed for human habitation, and safety features like sprinkler systems and fire alarms may not be present.
You may be able to find paid individual parking spots where camping is allowed using apps like Boondockers Welcome or Vanly. Otherwise, campgrounds are your best bet.
Some nomads have reported online that if your vehicle is relatively stealthy and you keep a very low profile, a parking lot owner or employee might just ignore you. Your low profile gives enough plausible deniability to say to their insurance company or the police, "I had no idea he was sleeping there? whaaa?!" if something happens. If you do get The Knock, be sure to leave right away and find alternative parking options. You may not be able to get a refund on any amount you had paid for the spot, since you would be in violation of the parking rules.