As someone who is going to Santiago as part of the program, I've done some research based on previous participants' experiences.
Find apartments using Home Chile (http://www.homechile.cl/) and all are furnished. Many recommended Providencia area.
Since you are based there, hope you don't mind if I ping you for questions.
matt
ps wasn't going to post this as a separate answer because it's 10 years old and i had a local job offer, but i found getting permanent residence to be very easy (i had arrived on a tourist visa, which can be renewed for up to 6 months). i can't remember if having the job offer was critical (i think it was the other way round - i needed the residency because employment would have been illegal on a tourist visa), but what surprised me was the need to show evidence of education level, so bring some kind of certificate!
From the Startup Chile FAQ, participants are entitled up to $600,000 CLP monthly spending on rental. Many had fully furnished apartments around Providencia with facilities like pool and gym (from HomeChile listings, apartments with such facilities are around 400k-600k). Providencia are also recommended because it is said to be safer.
PS: Another website similar to HomeChile is ContactChile (http://www.contactchile.cl)