Yeah, 20K will not get you far with new furniture. It really depends on whether your flat will already come with a wardrobe/closets. New, those can cost a bundle. A good mattress could easily set you back 10K alone. Of course, you can spend less at Ikea or on some Made in China bedding. If your employer is shipping things for you, then definitely ship the mattress.
As for a home entertainment system, just the words "home entertainment" conjures big bucks. Otherwise, as you said, if you buy stuff used, you can probably get a clunky old TV for less than a thousand dollars from a departing/upgrading expat.
Personally, I would not rent a furnished apartment. Local landlords have some of the tackiest furnishings I have ever seen, and they will skimp on all the fixtures. Take a close look at the bathroom and kitchen before you make any final decisions.