Also, try Airbed and Breakfast. It looks like many people rent short-term or for a few nights, but some also longer term.
www.airbnb.com/ Craigslist is usually cheaper, though.
Read the description well because a "family homestay" implies that someone in the family will pay attention to you, have time to spend and chat with you, presumably so you can practice Spanish and learn about them and their city, right? That is often not the case, even when you are renting a spare room in someone's house and even if they are home all the time. It is not uncommon for them to go about their day and ignore you, so be sure to express your expectations to the person beforehand so both don't end up disappointed.
I would not wire money to an individual ahead of time, maybe to a recommended agency. Getting the family your flight itinerary and any other info they request should be enough. You can always stay at a hostel the first few nights.
