Opinions needed on replacing factory speakers (4 door compact sedan)

Specs:

2006 Mazda 3 Sedan
- 5x7 / 6.5
- Kenwood 348U Stereo
- Factory speakers that distort heavily on some songs
- Do not intend to get subwoofer
- Budget = ~$400

I definitely want to get component speakers on the front doors with tweeters flanking my windshield. I listened to the Polk Db5021 or whatever at Fry's, and I immediately knew that's what I needed.

It begs the question of what speakers to get for my rear doors, or even both my rear doors and a pair behind the backseat (which I'd rather not cuz thats more $$$).

Polk's coax speakers don't sound like they can deliver the bass I want, but I am afraid to get two different brands of speakers.

I listen to rap sometimes, but im not looking for booming bass. I'm looking for crisp mellow bass that's just right.

In general, that's the type of sound I'm looking for. Clear, crisp, accurate, and life-like. As if you were sitting in the front row yourself whether its a saxophone, guitar, or I can hear the singer take a breath.