We have a condo that we rent through homeaway.com & we require all payments in advance. Every owner has their own set of terms. We require the second and final bill to be paid 30 days in advance. We do use a contract & make sure the owner you are dealing with uses a contract, it protects both of you.
As for checking with the management company, that probably won't work since the owner is renting on their own, they probably do not have a management company. You can call the homeowners association to confirm good standing and star rating if applicable. If it is part of a resort you can call the resorts business office to confirm the same details.
Try to get pictures if they don't post them, and if after talking to the owner you still aren't comfortable you could ask to call or email for references, or just move on to another owner. I don't think you will find an owner that doesn't require full payment in advance however.