I've rented houses several times in Florida (Orlando, Miami and Coconut Grove). My family also owns a rental in California, so I'm familiar with how the rental process should work.
First of all, stick with the well-know rental sites (VBRO, Homeaway, AirBnB). Look for a well-developed profile that includes pictures, reviews and a calendar. Look at lots of profiles to get an idea of what the rentals in the area are going for. If you see one that's way below the going rate, that can be a red flag. I also look for profiles that are well-written. I've seen some very poorly written descriptions that look like they were thrown together. Those just look sketchy to me. Also look for recent favorable reviews on the place. If the most recent reviews mention the same issues, the place might not be well-maintained.
I also think it's a good idea to correspond with the owner a few times before putting down a deposit. Ask a question and see how quickly the person responds and if their responses seem professional. We like to ask if the house has electronic locks and, if not, how we would get the key. We once stayed at a place in Coconut Grove. We arrived late since we flew in from California. The owner told us the lady across the street with the green driveway would be up and ready to give us the key. We got there close to midnight and the street was very dark. Even with the flashlights on our phones, we couldn't tell which house had a green driveway. We didn't want to just knock on a random door that late, so my sister called the owner. She didn't know the house number of the lady who had the key, but said another family around the corner had one. She called and woke them up to come to the door with the key. That was kind of weird. We decided we would prefer electronic locks where they just give you the code. We also like to ask if the house has a coffee maker and mugs. One duplex in Miami didn't have either!
The link you posted seems like a good choice. The house looks nice and the description is quite detailed and professional done. The reviews look good and there are several recent ones.