Paying cash for rental house vs. keeping cash for future home?

[Michael Zagorsky]

As some background, my wife and I are temporarily staying in our income property (paid off) for the next couple of years as we fix it up and travel almost full time. Our goal is to buy our long term permanent home when we find it, < 3 years from now. Our total guess is our new home would be $300-$400k range.

We have about $200k in cash.

The opportunity has come up to buy another rental property for about ~$90k.

So at a high level what are everyone's thoughts on whether it is better from a numbers perspective to have a paid off rental house vs. a (almost) paid off primary residence? Assume we don't itemize so we can't deduct mortgage interest. I know we can deduct mortgage interest from our Schedule E but getting a mortgage for rental properties seems to be at a higher interest rate.  

In terms of overall strategy, we are not looking to build a big portfolio of rental homes.  Longer term goal would be 3-5 paid for properties acquired over the next five or six years.  We do not want to go crazy with leverage.