$200 for everything is next to impossible in new equipment. You could check Ebay for used, but to some extent, with used equipment, you have to have enough knowledge to know what equipment is worth buying.
Both Polk Audio
n have EBay site where they are closing out products, you can find some real bargains there -
In an apartment, I would advise against a Subwoofer for music, unless it is student housing and other people won't mind.
These might not be too bad -
Bass response is not super deep, but you can't expect that from a bookshelf speaker.
I also disagree on the advice to get a cheap AV Receiver. You are spreading your already lean money much too thin on a bunch of amps you are not even going to use. Far better to find a bargain on a stereo amp.
This is a decent Stereo Receiver, but as you can see it kills your budget -
Though I might be skirting the rules a bit, I have one of these amps for about $100. I have the original box, so I can ship it. Probably only $15 to $20 to ship -
If a window pops up over this link, simply click the "X" to close it and you will be able to see the specs on the amp. The amp is in as near mint condition as is possible. I take very good care of my equipment. Fully functional, 100% working, I used it up until a few weeks ago when I bought a new amp.
Here are the specs from Onkyo TX-8255, 50w/ch, AM/FM -
You can see the amp here in my set up. It is the amp on the Left -
And you can hear the amp in this video -
The Yamaha amp on the right acts as a Pre-Amp for the Onkyo on the Left, but you are hearing the Onkyo Receiver driving the 12" DIY speakers.
If you are interested, I will pack it up and take it to a Shipping Store and see how much it will cost to ship, though I would need your location, really just the city and state.
Two other speakers that are nice but again pushing your budget to the limit (note price is EACH) -
Naturally the bigger speakers is also going to be the better speaker, though equally the more expensive speaker.
These Sony floorstanding are not the peak of music fidelity, but they sound OK -
The price is for a PAIR.
The BIC speakers are probably OK, and have fair bass response (price per pair)-
These Pioneer are on sale for $126/pr
Again, another pair of Sony that are probably OK -
But as you can see, for a total of $200, the best you will get is a boombox, though a Boombox may be OK for your needs.
I think you will get the best quality system, with either the Polk Audio Monitor 40 or the BIC which had pretty decent bass response for a bookshelf speaker, and either my Receiver or one similar to it. My advice, don't get an amp with less than 45 real watts to 8 ohms.