My estimate is that totals around $5600.
That sounds like a fair amount of money to drop all at once, especially considering all of the deposits you have to make when moving into a new address.
I think you should figure out
what you will buy when as you phase into it.
Personally, I want to have good SQ, so I might opt to pick up a solid but obsolete stereo receiver off Craigslist for $50-$80 and my permanent Mains (or Satellites, depending on budget). I probably would want a TV and see Flatscreens (in the 27" to 40" range) are starting to show up at Goodwill for under $100. The older flatscreens will have RCA outputs (or at least headphone jack) that can connect to old stereo.
Now you have good SQ for music in your house and can phase in the rest of your system. You can later re-purpose the receiver and flatscreen to the bedroom or something. Even if you took them to Goodwill, I'd pay <$180 to be in good SQ for several months-year while waiting for the bucks to get my real system.
The point I am making is you can pick up some temporary gear at the "bottom-feeder" prices to complete your system for very little.
It is obvious that you don't need to get subs until near the end of building your systems. By then you will have experienced apartment life with your neighbors and figured out what will work for your situation.
I might keep my eyes open for a used 10" sealed sub and not get into ported subs until you leave the apartment. Again you could apply the small sub to the bedroom system later.
If you are carrying a big wad of cash from your last location...nevermind!