I can't find any technical specs on that particular motherboard model. If it has a Realtek audio codec and you're looking to buy high-end headphones, you want something like a ALC889, or higher. Not a big issue - if your laptop isn't older than 5 years and not super low-end you should be safe.
The human ear struggles to hear any frequencies above 18 kHz, so don't bother wasting hard drive space on audio files with a sampling rate 192 kHz. As long as you're listening at a sampling rate of 44.10 kHz and a depth of 16 bit (Audio CD quality) - you're good. Higher sampling rates are only relevant to professionals who do the actual recording, mastering, mixing, filtering and so forth.
Ideally you want to listen to your music in uncompressed format, that is FLAC - or directly through Audio CD. The bitrate of your average FLAC file can vary from 200 kb/s to well over a thousand, depending on how much information the audio recording holds. A higher bitrate doesn't necessarily mean higher quality; some music is simply more silent and low key, thus holds less information. Your average uncompressed track will have a
variable bitrate of roughly ~900 kb/s. Just for reference, YouTube generally encodes the audio of the uploaded video file to 126 kb/s AAC, but - because of this particular compression - the bitrate is
constant.
Since Windows only gives you a limited amount of information on audio and video files, you might want to use an external tool like
MediaInfo. Free and never more than 2 clicks away from a detailed insight into your media files.
How much are you willing to spend?
How important to you are noise cancellation, weight, mobility (ability to fold, removable cable), materials, sturdiness etc?
If you're like me and predominantly use your headphones at home, I wouldn't look too much at mobility and weight. For me it's all about the audio standard and the build quality. Real leather and as little plastic as possible, preferably aluminum.
We could look around for a nice pair of cans that don't require an amp to excel on a low-power device like a laptop or smartphone.