I have always thought that it would be pretty cool if Axiom had car audio components. Better yet, if they partnered with some manufacturer to put an Axiom system together in a vehicle as a high-end audio option. What a way to advertise! I know, I know, I'm dreaming.
Back in the day when I put a lot of time into car audio, I had consistent good luck with Polk speakers. To me, they always seemed to sound just a little bit better (cleaner) than comparably priced Kenwood, Sony, Pioneer, etc speakers. I also had some Eclipse speakers that were really great, but they weren't cheap. I never owned a set but I had a friend with Boston Acoustics speakers that also sounded really nice. This was all 10-15 years ago, so times & brand quality may have changed.
It's hard to just blindly recommend components, because there are so many variables as far as what speakers will fit in what you own, and how much work you want to put into it.
Generally, assuming a 'standard sedan' sort of layout, my advice would be to start with a nice component set for the fronts. This will be a midbass driver, a crossover network, and a tweeter. IMHO, component sets generally produce a much nicer front soundstage compared to just a coaxial speaker in each front door. A little more work to mount the tweeter & crossover, but great sound in the end. $200ish for a nice set.
Then pick up a pair of coaxial 5.25's or 6.5's (or 6x9's) for the rear, of the same brand/model line as the component set. $100ish.
Then pick up a little 4 channel amp to run it all. 60x4 or 80x4 would be sufficient, I'd think. $200.
That leaves $500 for a powered sub. Since your goal isn't to remove people's fillings, but to have pleasant and appropriate levels of bass, a nice little self-powered 6.5" or 8" sub would work well. Something like a Bazooka or an Infinity BassLink. Many choices in the $300-$400 range.
Good luck, and have fun!
