I agree with most of the previous answers. But, there are more questions to be asked to properly determine the answer that is right for you. The question you asked is which one should you purchase first. There are two parts to that. Financed or cash, and primary residence or investment. A conversation with your accountant or other financial professional may reveal the best strategy. It most likely will be best to finance the first property, if only to have a clear financial picture for the lender. That being said, your financial counselor can tell you whether financing your personal residence or investment property will make more sense for your particular finances and taxes. You don't mention if you already own your own home. If you do, will you need to sell it to buy another, or will you maintain it as a rental? Many lenders are more tight on their lending criteria. If you buy your investment first, a lender may not look at another property seriously as a owner occupied vs. investment. Additionally, if you buy a lender owned property, you need to make sure that the property you choose as your primary residence will indeed be used for that purpose. Many lenders require a disclosure to be signed stating as such.
It may seem like a straight forward easy question, but there typically are more details to determine what is right for you and your personal situation. It isn't one size fits all. A proper answer comes with a full discussion of your needs and wants. I hope this is a help to you.
Adam Tarr PC
CItywide Real Estate