Dc for power supply

An interesting question. I personally don't think that there would be any sonic difference in batteries, especially when using them for just the filaments. However stranger things are known to occur in this hobby. The use of batteries keep popping up in conversation to power audio gear. I.E. Southerland, Vinnie Rossi and Stromtank to name a few. 
I myself keep toying with the idea of installing a solar array to maintain the charge on a set of car batteries (installed outside).. Then using a pure sign wave inverter to produce 110VAC to power my system.
Got the idea from  my APC S15BLK power conditioner. It has battery back up with pure sign wave regeneration. Upon any main power disruption the battery backup kicks in. Even with the smaller batteries in the APC it can run my system for a very reasonable time. 1-2 hours.

 dc filament on a cd player

- eh?

you can certainly run a car stereo off a storage battery - what components are you planning to use?  (not a Class A tube amp, I hope)

any commonly available battery chemistry should be fine

I'd say it would be pretty pointless to use batteries for filaments. As long as we're not talking directly heated tubes you might as well use AC. It makes no difference. Having a constant temperature is far more important than how clean the power is to an indirectly heated tube.