As above the main question is why, due to the headunit being integrated with the car settings it's tricky to upgrade without spending quite a bit of money, I think only Alpine makes a headunit that can be replaced which keeps all the current functionality of the car but it's about £800.
You can do a little or a lot it just depends on your budget.
Even if you don't have rattles sound deadening the doors first will make a big difference to the current sound quality.
Then if you want better quality look to replacing the speakers with better ones to run off the head unit, although to get the best out of them will mean you will need to add an amp or 2 and you will then also be able to add some subs, however you should hear some improvements just by changing out the stock speakers.
To do this you will need amps that have speaker level inputs or invest in a line out converter as there aren't any pre-outs on the headunit to connect to the amps, some are cheap and others are expensive.
Don't forget all this will need wiring in via the battery so will need a lot of the trim removing as well and splicing into existing wiring.
After this you're looking at custom builds and system tuning and higher end components which is ££££.
If you just want to do a slight upgrade I'd recommended just sound deadening all the door cards first and see how it sounds and then maybe look to change the stock speakers to some better ones, this should all be doable for around £2/300 odd, after that it does start getting expensive.