Thank you Zoot.
You have a nice system, so you will likely be able to hear differences in the computer you use (I'm still making very many assumptions here, but I guess that's the nature of the fora).
However, you also say you are not very computer savvy. And believe me, computer audio can get utterly frustrating at times when we don't understand why the darn thing ain't playing music! So it's about striking the right balance. We generally strike for balance between price and sound quality, or ergonomics and sound...well, here we also go for frustration and sound quality.
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The easiest thing is to use a laptop connected to a good asynch USB DAC. It's easiest because the keyboard and screen are always available, and when you get to that moment when you don't understand why music is not playing it is just very convenient to have the screen immediately available. Of course, this comes at a sonic cost: you will not be able to use audiophile USB cards on a laptop, plus the screen does generate RFI (and even when the screen is off, the video section of the mobo is still active, which generates jitter). By the way, jitter is the computer audio evil. You want to minimize it as much as possible.
Also laptops have fans. Some are noisy in that you can hear them. All of them are electrically noisy: their motors introduce jitter, which is also why people recommend replacing the hard disc drives with solid state drives - to get rid of the motors. Of course, speed is improved, but to no sonic benefit, I think.
Another aspect is how you will store the music. It's generally a good idea to use a small internal drive, if solid state, the better, to host the operating system and the music player (example: JRiver), and to keep the music in an external drive. Some people use a network attached drive (or NAS). I will assume you don't have one (me neither). The sensitive piece is you don't want to use a USB port in the laptop to connect a HDD and another to connect to an asynch USB DAC because USB stands for universal serial bus...so being serial you have now a streaming process (meaning rwal time) and a data transfer process (music data giles from HDD into processor), and that introduces jitter.
YOU CAN use it this way, it is only that it will not yield the best sound possible.
Very few laptops these days come with a firewire connection, and some have thunderbolt, which are just a couple of non-USB ways to connect a HDD. So I would look for a laptop with firewire or thunderbolt, and an asynch USB DAC.
Some DAC manufacturers, such as exaSound, build their DACs to be "immune" to the feeding computer. This is generally marketing BS, but some report exaSound DACs to be insensitive to the computer. Ao one route is to go with a laptop to make it easy, and if you want to upgrade your sound go with one such DAC. I don't believe the Musical Fidelity M1 is such a DAC, though.
Oh, and wifi also introduces jitter. So you want to turn off wifi when you listen to music. It will act like a CD player of sorts: a standalone unit you need to stand up to to select the music. Or you can live with the jitter and be more comfortable :-)
BTW I use a wifi bridge here, so I have wifi turned off but the computer still has access to internet.
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The other approach is a PC. This allows for a lot more flexibility for now or down the road. "Ideal" or "best" means different things to different people, and in different fora, but let's say AudiogoN is not really into specialized PC audio, so allow me to say that the best result would come from a PC that:
Has no cooling fans. Again, you want to avoid the noise you could hear, but also introducing jitter through the motors. You can use the Atom processor or the NUC within this budget.
Allows for connecting an audiophile USB card. You don't want to use one as you get started but leave your option open for later. Not sure if the NUC allows that.
Use one small SSD for OS and player. For this one you get the smallest drive you can find as it will be too big anyway. Another drive connected through SATA to the mobo to store the music. A large SSD is expensive, so I use a large HDD fed by an independent power supply (to avoid introducing jitter) and sitting outside the PC in a heavy enclosure.
This server runs "headless", meaning you use a screen for setup, then just turn it off and don't use it again. Same with keyboard. You want to disconnect them from the mobo, so when the server starts it doesn't sense the screen and the video portion doesn't activate. On a daily basis, you simply turn on the server, and control it from an application on an iPod/iPhone (JRemote for Jriver), or from an android phone/tablet, or a multipurpose laptop.
Power supplies. This one can get really complex. Lately some folks are powering the internal clock directly...way cutting edge for me...and too complex. But using a linear power supply is definitely a good idea as the switching mode power supplies (SMPS) generally introduce significant jitter. Then, another step is to independently power your OS SSD with a battery or linear PS, same with the audiophile USB card...you can see how this can go nuts pretty fast. I would start with just whatever PS is provided to you and eventually upgrade to a linear PS. Later, if you are so inclined, inquire about next steps.
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Sorry I got very long-winded, but I wanted to give you a good flavor of what entails the big choice you need to make now: laptop vs desktop. The CAPS v3 I suggested first can almost be as simple as a laptop if you happen to have a screen nearby, and would get you started, and gives you some choice for upgradability.
For what it's worth, I started with a very old Win XP laptop with an external USB HDD with the music, connected to my asynch USB DAC. It clearly wasn't optimal and I knew it, but I got a feeling if computer audio was for me and how willing was I too get into the deeper. So please don't take my words as some sort of either you do it non-audiophile grade or you have to go into the deepest. There are very many shades of gray in between and you need to think what works for you today, and later think again if you want to go further.
Cheers!