generally onboard audio is good enough for most people... unless you're experiencing an issue or are an audiophile onboard might suit you. your onboard is only fair quality its certainly worth at least looking at other options even if they arent strictly required. there is no need to spend $250 on a soundcard for the situation you describe... something like the xonar DX which is less than your proposed budget would work fine as it has the same DAC chip as the $200+ stx (it doesnt have the amplifier, but you dont need that).
if you ran a digital signal direct to the receiver (spdif optical, spdif coaxial, hdmi) it would decode the signal using its own DAC instead of your pc. there is still the possibility of distortion when encoding the signal, but generally this is more an isolated problem instead of the majority so you should be fine.