Residing in high-tax New Jersey and working remotely, we’re exploring strategies to reduce our overall tax burden.While I’m intrigued by the short-term rental strategy, my preference leans towards LTR due to familiarity.

Also the best businesses have some sort of a market budget typically.

Heres the situation, and let me know what things to look for, how to come about this situation, what could be the best possible strategy to use, etc. 

Look for properties with potential for rental income that covers expenses.Long-Term Strategy: Plan strategically for future moves, leveraging VA loans and other financing options to expand your real estate portfolio while maximizing rental income and equity growth.By strategically managing your current properties and leveraging financing options like HELOCs and VA loans, you can effectively expand your real estate investments over time.

Yes, we have a few different accounts 1. operating expenses for the business 2. one account where all rents and cash reserves for maintenance are held 3. security deposits 4. company taxes 5. company savings 6. company salaries, etc..

Even if you create a non-CA LLC, if you are managing the business from California, you will likely be deemed to be "doing business" in California and therefore likely subject to CA taxes.

the permit or business license or both?

Leasing it out via Airbnb or Vrbo is an option if available and demand is there.No creative buying strategies needed.

What are the best strategies you would advise to newbies and wish you knew when you started?

This isn't a personal relationship its a business one.