Stock sound systems are decent quality. It's great enough to satisfy the average listener. But they don't produce the low end and the high end very well. Part of your music is just missing because the system cannot produce it or it's just not heard. When most car audio enthusiast buy a new car, we immediately tear out the stock sound system.
Improving the sound quality in your car comes to a big budget. If you got the money in your wallet, spend around $1000 to $1500. If you have a huge bank account to drain, I'd spend $2000+. These will include a high quality 4 or a 5 channel amplifier, a high quality monoblock amplifier, a high quality subwoofer, coaxials, components, 2-ways, 3-ways. You will also need to invest into a proper enclosure for the subwoofer. A $300 subwoofer will NOT perform well in the wrong type of enclosure.
The electrical load that you put on your vehicle's alternator can only handle so much. If you're going to be running a 1500+ watt RMS system, you need to upgrade to a high output alternator. The next thing that comes into play will be the big 3 upgrade. If you have no idea what the big 3 is, search it on Google or YouTube.
The cheap stuff is cheap for a reason. You're going to need to spend at lease $200 for a quality pair of speakers. Stock speakers provide pretty decent quality. Your sound quality is only as good as your speakers are. If your speakers are poor quality, then your sound is going to be poor quality.
Most aftermarket speakers need at lease 100 watts RMS to perform well and loud. So if you're going to be powering a $150 speaker off a 20 watt head unit, it's not going to perform well and loud. Most subwoofers need at least 1000 watts RMS to perform well and loud. I'd look for a single high quality 12" or a 15" subwoofer around 1000 watts RMS.
Once you have a quality system, you'll be the number 1 guy at the car audio show!