More importantly, whether or not you use a Corp or an LLC, you will have to get approval beforehand by the bank to buy the property through an LLC/Corp structure if you intend to use a mortgage, or afterwards approval AND file a with the court to legally change ownership afterwards. Either way should be no problem if you are plunking enough money down, but be aware that although it offers you liability protection, either one (LLC/Corp) also increases the tax-filing hassle factor.
Another way you might consider is to max out liability on your home, and rental, and then ask for an umbrella liability policy. They might require that you park your car insurance with them as well.
I disagree with Delaware or Nevada filing because then you have to file taxes from those states, and beg for authority from NYS to operate here. If you are forming a company to sell the newest hottest widget, maybe...but for liability protection for rental properties probably not worth the hassle.
Antolin Du Bois, CFPÂ®