There is an MLS system here called "house on line" but it is subscription based and limited to realtors.. so working with a formal realtor gives you access to a ton of properties. Other than that, there are the online classifieds like "a donde vivir".
Regarding construction.. I know people who have built their own house (rather.. had someone build it, but they participated in the planning). It is an option, but I think you would want to be very comfortable with the system here (and the language) before launching into something like this. I sure wouldn't do it. Seems like a lot of risk, and probably a lot of time.