It kind of depends on what your speakers are. Then what the True RMS and Max RMS.
I don't want to say that Any speaker upgrade to the Factory speaker is an UPGRADE. However that is the Fact.
So you say your speakers are in and it sounds better! That is great and a good start! Did you use any type of Frame or did you Seal the Gaps?
IF this was my car and I was doing the UPgrade... Here is what I would do. Not saying you have to by any means....
Upgrade the Wires for the Speakers with 16awg. wire. (I would pull in new wire if I was going to do a new head unit to the dash.) If Amp install to the Amp Location. So There is going to be more wire needed for going to the AMP...
Next there is a Need for a Crossover for the Front Stage. Seeing the Car OEM radio runs them crossed from the amp n the trunk....
you can get the crossover for passive or active both will work well...
Then there are other things that you can factor into your new install... Do you want just normal 4ch or would a 4Ch Bluetooth better suit your needs? If you don't want to add a new Bluetooth deck or use a FM modulation for your Bluetooth then there are some Bluetooth Amps on the market... One if your speaker is able to take the power is REAudio BT-900.4 It will do 80 Watts a Chan or more running 2 ohms and even more Bridged. They are nice amps but there are many options out there... I have been a Fan of REAudio since back in the day when they were USAMPS. They have Great THD and the watt ratings are not based on what we would call ILS... IF Lightning Stikes lol... I mean when an AMP says it can do 400 watts and you connect it to a Speaker that can take 400 watts but can't even power the poor thing...
In the end. How many watts can the speaker take? Brand of Speaker and type of sound they should produce. Don't go cheap on a Amp or an Amp install. Treat your Speakers nice and they will treat you nice back

To low of power can be just as bad as to much for a Quality Speaker.
James