I would advise going with a different mp3 player. A lot of people on the web seem to have issues with making the walkman interact smoothly with audio programs.
If you want that particular mp3 player, here's how to make it work with ubuntu:
http://ubuntu-virginia.ubuntuforums.org/showthread.php?t=866297
Otherwise, I'd recommend a generic used iPod nano/classic/touch. They are almost always perfectly compatible.
Good Luck!
EDIT: Additional How-To: kubuntuforums.net/forums/index.php?topic=3096598
When I bought mine, I simply brought a live CD in the store, and asked to try it on their laptops. I explained them what this is, and that I want to check the compatibility of the different components with Ubuntu. I sometime had to explain what Ubuntu was...... One place told me a flat NO, that I could not try it. I ran out of the store as fast as I could. At the store where I actually bought my portable (in Dec. 2006), I tested that the display was actually working on the internal monitor, at the full resolution, as advertised on the spec sheet, that the wireless adapter was found, and that I could use the card reader, with a card I brought in. I finally tested the sound itself, which was rather easy to do.
Today, you could bring Linux on a USB disk instead, or even an SD card. Also, in 2010, you should expect every sales rep on the floor to be at least know about Linux. Usually, they should understand that starting it from a CD, especially if this is a branded one, not burned at home, there is no harm that will be done on the machine.
NOTE: The fact that some components are not discovered right at boot from a live CD does not mean that Ubuntu will not support it. Chances are that you will find the proper driver for it. You will just have some manual setup to do.
You may also want to note the brand names and models from a store and check on the net, with Google. You should usually find either some test cases or message exchange about it that will give you a good idea about the model you are looking for.
Best Answer
Try it out.
This is the only real answer — there is enough variation in hardware specifics (even in a given model), and software changes too often, for any specific answer to remain valid long enough. Conversely, the many different components involved can cause many, different and unrelated, problems, so a post about what will happen with a specific device doesn't fit well with the Stack Exchange Question & Answer format:
We can't handle open-ended questions about what problems you could face, but questions about specific problems are much better.
Live
You can make a bootable USB from the Ubuntu installation ISOs, and then try out a live session instead of installing. The live session doesn't make changes to your system by itself, so it's a safe way to test drive Ubuntu. However, even a successful run of the live session is not a certain indicator - there have been cases where the live session worked fine but the installed Ubuntu didn't.
Now, proceed to the first few steps of: How do I install Ubuntu? You should see an option to "Try Ubuntu":
Once the live session starts, play around a bit with Ubuntu to see how much of your hardware works and how well it works. Try to narrow down any problems that you faced, and post individual questions with relevant details. Then we can help you with the specifics.
What follows is a set of links, both to posts here on Ask Ubuntu, and elsewhere, that can help you in your quest. I'll try to avoid passing judgement on any particular manufacturer, but instead try to link to canonical posts that's likely to be kept updated. The major tag for each section is also given next to heading, use them when asking questions. So, for example, a WiFi problem with a Qualcomm Atheros chip would be tagged networking wireless atheros and include the output of the wireless info script.
Common problem points
Hardware support can be hit and miss. It is helpful if you can lookup the exact hardware configuration of your system (i.e., not "3GB graphics" or "Killer WiFi", but "NVidia GTX 670MX" or "Qualcomm Atheros QCA6174 802.11ac" - the exact model number is important).
Dual-boot dual-boot
UEFI uefi
Recent releases of Ubuntu tend to play well with UEFI. See How do I install Ubuntu alongside a pre-installed Windows with UEFI?
Networking networking
WiFi wireless
Post a question with the information from My wireless/WiFi connection does not work. What information is needed to diagnose the issue?
Broadcom broadcomEthernet ethernet
Graphics graphics
NVidia nvidia
AMD amd-graphics
Intel intel-graphics
CPU cpu
Intel intel
ARM arm
If you have an ARM device, these might be informative:
Fingerprint reader fingerprint-reader
Webcams webcam
Integrated webcam not detected after update to 14.04
Webcam (Ubuntu Community Wiki)
UVC driver homepage has a list of all officially supported webcam models by this one universal driver.
SSDs ssd
Touchpad touchpad
modprobe
to activate your touchpad.Sound sound