Hi all, thank you Epicatt2, Luna, Costaricafinca, and JulieH for all your advice and the information!! I really appreciate it.
Eleanorcr, there's no need to attack me. What do you mean I know all the answers? Yes, we do plan on moving, no, we are not sure the best way to do it. Hence the questions. Thank you anyway.
Anyway, it is not that I am overly "squeamish" about the place. I don't care if someone seems like the nicest person in the world online, I will not trust them 100% unless I know them personally (or know them through a friend, that is also better). Therefore, I want to go about doing this the best way possible.
This place seems very nice online, there's pictures, the contact was very polite, and deposit is completely understandable as it would be in any place, whether in Costa Rica or not.
We agree that we would eventually like our own apartment, but, as was mentioned earlier, yes, we do want that comfort of being set up already. Especially having a cat who does not in the least bit like to travel (although I'm glad to read that it should be easy to get through the airport with her) we want to have headquarters when we get there, which will allow us to be able to focus on job-hunting for the first month.
After much looking, we both like the location and place that we have chosen. Not to mention that if we are unsuccessful in finding jobs, we won't be able to stay anyway, therefore we just need these temporary accommodations until we get settled in, then we can decide if we want to move or not. And Costaricafinca- having or not having a job will influence us a bit, but not too much. We're on a tight budget, and will be trying to stay in the cheap range, regardless of whether we find jobs or not (since as I've been warned if we find anything we can expect low pay).
Thank you again so much everyone for your help, I will look it all over in detail tonight!