What's the output of the existing head unit, I'm going to be it's 20W/channel (RMS), which in my opinion/experience, is more than enough for casual listening, with decent speakers. Notice that underline. You're looking for (I would be looking for) coaxial two ways in the same size as the factory speakers, forget about separates (yes, those omnidirectional tweeters are a no-go), and forget about speakers with "high power ratings". The greater the power handling of the speakers, the less efficient they are, and the more power you'll need to drive them.
Why do I say no separates - first, separates need a crossover, good separates will have more than just a capacitor inline with the tweeters - second, mounting of the tweeters, you're going to see a lot of tweeters, even in high end factory systems, mounted on the sail panels (triangular piece on the inside of the side mirrors), the problem is that the greater the distance between the tweeters and the mid ranges, the less coherent the sound image will be. Speaking of mounting, you're also going to need to find a place to mount those crossovers.
Get a tape measure and measure the distance from the passenger side mid range to where your ear would be and then repeat for the passenger side tweeter, see the difference? Now repeat the exercise on the driver's side, the differences in path length are huge on the driver's side, mid range is almost double the tweeter isn't it?
If you want a coherent sound stage, you want the mids & the tweets together, and co-axials is the way to do it.
What was that? You don't care about the sound stage? You don't even know what the sound stage is?
The idea behind "HiFidelity" stereo systems is to, as accurately as possible, reproduce the music, the various instruments, the vocalists, what ever genre appeals to you, and when the mids & the tweets are separate, the lower notes from any given instrument don't arrive at your ears at the same time as the higher notes (including harmonics of the lower notes) from the same instrument, this causes the "position" of the instrument to be constantly moving.
Quite a few people don't care about the sound stage, they don't care about a flat frequency response, they don't know what the music sounded like live, so it doesn't matter to them. How do the high end factory systems with sail panel mounted tweets deal with this, by electronically adding delays, vehicle manufacturers pay big money to the big names in audio systems to develop and tune the drivers (which are "handed" by the way, not the same left & right), and the head units to get what they want, and then they charge the owners. accordingly.
Why am I steering you away from an amp, even a mini amp - in a single word - wiring - you're going to have to find a suitable location for your amplifier, run cables from the amp to the existing speaker locations, run power cables (nice heavy ones) to the amplifier, and then run cables from the amp to the head unit to drive the amp (does the head unit have RCA outputs, they are not common on factory fit, and if it doesn't, you're going to need impedance converters, or an amp that has high level inputs, just typing that gives me the heebie-jeebies)
Confused much now?
Keep it simple, you say you're looking for a modest system, stick with the factory head unit, add an active sub, and decent speakers, down the road upgrade the head unit. As I said earlier, it's very difficult to achieve high fidelity in a car, you can however spend a ton of money trying - you're not interested in high fidelity, you just want easy listening, on a budget - well that was the recipe I just gave you.