@Ryan Beasley First question, have to shot photography before? Any type? Are you familiar with jargon, basic techniques, camera settings and the exposure triangle?
I've shot many properties as an architectural and real estate photographer. I will assume you are knowledgeable on photography. There is no best camera, it's how you use these "tools." You can utilize a canon, nikon or sony body and pair it with a decent wide angle lens. If you get a crop sensor vs a full frame, you will have to get your lens for optimal focal length. Read the review on image quality. Then there's the actual art of capturing the property using flash, HDR, flambient (flash and ambient blend), and other variations.
$1000 could be tight to get a basic camera body, lens, speed light and a tripod depending on what brands and quality gear but it's doable. My advice is to get used if you can from Adorama, B and H Photo, Roberts Camera or KEH.