I spent $425 on a used Musical Fidelity A220 integrated amp, and I love it. If you're running the XBox using a digital connection to your amp, you're probably going to want to find an amp w/ digital inputs... the amp I listed above doesn't have digital inputs, and my former tube amp didn't either.... would need to add a DAC.... DAC is going to cost some scratch... or you could rely on the analog output from the xbox.
at any rate, the way I see it is that you just bought new speakers, so you don't want to replace that. The XBox is quite unique in its abilities, so you probably don't want to replace that... which leaves amp.