Depends on how comfortably and conveniently you want to live. You could probably find an older, one studio/BR apartment for under $1000/mo. If you want a secure building, with secure parking, a pool, gym equipment, etc, it will cost more. Furnished places tend to cater to the professional crowd and won't likely be a better deal than having it paid for directly by an agency (but I could be wrong). Of course, if you want to live in a popular area or a very nice neighborhood, it will cost more.
Where will you be working and how far are you willing to commute? Some areas can get pretty pricey; but depending on traffic flow and where you work, it could be worth it to avoid a miserable commute. Without having spent time in a particular area, though, it can hard to know what the reality of traffic to and from work is and what the neighborhood is really like. Hopefully, an agency would set up it's workers in very convenient and safe places. While there's probably lots of potential for finding a better deal on one's own, I don't know how well someone can realize that potential on a first agency assignment to the area.