elmoe
Formerly known as JashuganHeadphoneus Supremus
The answer to that is a big, resounding yes! if you want to hear the utmost sound quality, then only a CD player plus amp combination will achieve this.
A PC/Tablet/Smartphone plus a standalone/portable amp (as long as it's a good amp) will be good but it will get you no where near the level of sound quality possible that a CD Player plus amp can achieve. With the money you have available to spend, you could build a phenomenal CD Player + amp + headphone system.
Care to expand on the science behind that? A CD player is not any better than a PC/Tablet connected to an external DAC, CD players just have the DAC built in. If you rip a CD to lossless formats, you are getting the exact same digital data.
heidimilk: The RME ADI2 DAC is a great DAC/headphone amp loaded with features that make it a very fun unit to fiddle with and get great sound quality. I like headphones that tend to be regarded as "bright", so I also use a tube amp to smooth things out, but the RME's headphone out is top class and I don't doubt pairs up well with an LCD-2.