Replacing "primary" residence with a new house while keeping the old one as "rental property"

Situation:We currently own a home with mortgage paid off. This is our current primary residence. Let's call this small/starter "Home A"

• We own Home A outright (no mortgage)
• We want to buy Home B and get a mortgage for it
• We plan to:
  • Move into Home B as your primary residence
  • Convert Home A into a rental property

We would like to get a 30 year fixed to purchase a larger home (Home B) and keep the "Home A" and rent it out and make "Home B" our new primary residence.

Long term goal, move back into "Home A" when we retire as empty nester...we like the location. Basically, we plan to "rent" from the bank a larger house while the kids are home and don't plan to pay-off the mortgage on Home B. Maybe at most stay in Home B for 20 or so years... and sell it and pocket any Home B $appreciation.

Question: When we apply for a mortgage, would we be applying for a "second" home? Would this result in higher down payment and higher interest rate, since its a "second" home?

What are some tax/financing strategies we can use to our benefit?

Thanks