IPod classic question

I'd say aux would be your best bet but I don't really know. It's a problem many users face and it'll be interesting to see what opinions you get.

Your music will sound horrible through an FM transmitter, even if your ipod files are high bitrate or apple lossless, and even if you have a better sounding car stereo.  In my opinion the FM transmitter is an absolute no-go for music, as you have discovered yourself - it doesn't even take a good ear to notice the severe degradation in sound quality.  You should definitely pipe your audio directly in using an auxiliary input, which it sounds like your car does not have in the obvious dashboard area location.

You should see if your car's (I'm assuming you have the factory head unit in your car) head unit has an auxiliary input in the back, or if you can get a harness adapter on crutchfield that will let you pipe your iphone signal in through either a line out dock or from the headphone jack.  Check on line for your car/stereo model.  Most newer car stereos have some way of bringing in external audio - this will be your cheapest option to get decent sound out of your ipod in the car.

If you end up upgrading your car stereo, there's nice head units that actually use a data connection with the ipod and do all of the audio processing internally - some of these can get expensive but also will sound really good - potentially much better than from the headphone jack or line out dock.  I have a kenwood excelon deck that cost about $200 which does this and it sounds pretty amazing plus provides full controls for the ipod.

Good luck!