When I read your question, I assumed you were interested in purchasing a condo that you could use and rent out as a vacation rental, rather than a permanent rental. In my neck of the woods, vacation rental companies charge about 30% for their services vs; 10% for permanent rentals.
As a loan officer, I see comparable rates to loans for investment properties and 2nd homes, with the single difference being that the points on the loan are higher for investment properties which you can mitigate with a larger down payment.
If you care about your tax deduction, you need to ask your accountant about "Aquisition Indebtedness". As it turns out, the interest deduction you are allowed has to do with aquisition indebtedness. Aquisition indebtedness is the lowest you've paid your mortgage down to - in your case down to 0, plus the amount you can prove you spent on rennovations, plus $100,000. So if you haven't spent anything on improvements for your TX house the maximum interest payment you can legally deduct would be the interest paid on up to $100K in new debt. If you need more than that to buy the place in SD, you should definitely think about financing it.