The term you should be googling is "silent install" rather than "unattended install".
Most likely you're looking for MSI based installation which can be silently installed by
MSIEXEC /I file.msi /QUIET
For non-MSI installs, you can either repackage them or follow the documentation for the specific product.
Virtually any software company will be able to provide you with the instructions for unattended installations of their product, best practice would suggest contact the vendor first before trying your own approach. Your "homegrown" solution might not be tested or supported and may provide problems down the track.
Last for WinAmp I'm not sure about silent installs of this, I think they use a non-MSI format so my instructions won't help much :)