As you noted the sound system is weak, so you must come up with a budget and plan around your taste of music. Some people want a million gigawatts of bass, while other want sound quality.
The generic answers are to replace your existing sub with Kicker ProComp 6.75". Replace the overhead pods with 6.5" Polks, and the fronts with 5.25" Polks. Polk DB series. Crutchfield should have them.
To me, you need an amplifer to go along with this upgrade, so if you want to go that route, and have room in the budget, I would upgrade that. Either a 4 or 5 channel amplifier, small one will fit under the steering column hidden away.