You can get rid of the hum from inverters by adding a couple large capacitors to flatten out the "ripple" in the half sign wave DC that it produces. Manufacturers do this for sound system quality power supplys.
I have a Radio shack 12 volt converter that is about 50 watts (12 v X 4.2 amps) and it has caps in it. The last stereo I hooked to it for testing was real quiet in its static condition ( on but with no signal to drive the amplifier : static condition )
50 watts may not be enough to support the stereo you have and may cause "clipping (like a brownout) in the system.
I have used freebie stereos from the junker cars I have had in the past years,at times I have used a small battery charger and a car battery to run it, but it is hard on a regualer battery.Deep cycles work well, but I dont usually run across one of those, at least for free
You can build your own power supply with a transformer, a rectifier setup and some big capacitors.