Hi Matt,
First off I think you have a solid plan in place. As you stated, I would pay off your debt and start savings as you are going to want not just the down payment but also reserves. Having 3 - 6 months of payments in reserve would be ideal at purchase. This will really depend on what you are comfortable with, what your lender will require, and what condition the property is in. If you are having to lease up the property, I would want more reserves than if 3 units are leased for the next 12 months. Finding a 4 unit that cash-flows is pretty tough but not impossible. I would speak with a Lender and find out exactly what type of financing you can get to start. This will help you narrow down the property you are looking for greatly. This will help you answer 1)What type of property you should be looking at 2)What price range you should be looking at 3) What kind of cash flow you need 4)If you need to bring in a partner. And honestly, there is nothing wrong with taking some time to build up your cash while learning more about investing. BP is a great place and I would recommend taking the BP House-Hack Bootcamp. I thought there was a lot of great material and even better connections to make!
Good luck!