A different point of view:
Even a modest set of speakers can sound pretty darn good when supplemented by a proper subwoofer, especially if you can EQ the tunes you are feeding them.
Most stock speakers are not that bad, but get overtaxed by doing work they are not designed for, along with sometimes being made to sound bad due to poor location choice. Most people could not tell the difference between stock and upgraded speakers (when properly EQd) unless the stock ones were SO shltty that they could not even be EQ'd to sound "flat".
On that budget and with careful shopping, you could get a decent head unit that has DSP correction, plus a sub and amp.
Buy it from the right store and you could get free head unit install plus wiring to mount the sub for about a hundred bucks.
Will it be a show vehicle? No.
Will it sound 100x better and give you lots of smiles until you get rid of car or decide to do little upgrades here and there? YES.