I suspect that the most significant factor affecting the sonic quality you will end up obtaining is the quality of the A/D (analog-to-digital) converter that is used. And although I have no directly relevant experience, I would be skeptical of the sonic quality of the A/D converter that is built into laptops or Mac Minis.
Also, what might be a good alternative to purchasing an expensive stand-alone audiophile-oriented ADC is to purchase a professional digital recorder that records to flash memory cards. You would then transfer the digitized files to whatever computer you use for playback. Such devices are made by, among others, Tascam, Marantz Pro, and at higher price points Sound Devices and Nagra. B&H Photo Video (bhphotovideo.com) carries many such products.
Good luck. Regards,
-- Al