Computer speakers, no, not a good idea.
Totally depends upon what you really want and how much is your budget.
A Yamaha speaker and sub-woofer system would be great but that will probably cost more than your keyboard.
Have a look at a pair if 5” M Audio or Mackie speakers both have been often suggested here.
I use a pair of Behringer 8” B108D speakers which I am happy with.
When you do get a pair of speakers if they are still a bit limiting for you the next step would be a Parametric Equaliser (similar to but better than a more usual Graphic Equalizer), this would receive the outputs from your keyboard and then the output frrom the PEq would go to the speakers and a decent PEq would also have an output for a Sunb Woofer if at some stage you wanted to add one.