one of the biggest parts to deciding which parts, is budget, how accurate do you want it to be, and how good are your ears at hearing. it will take months, usually years, for someone working with audio to develop good ears.
you will want to find equipment that is described as accurate and/or neutral. meaning the equipment (speakers, headphones, sound-card) isn't changing the audio source. there are several websites that do gear reviews, some even use eq charts showing how much the original audio is being altered. most speakers and headphones will change the audio to varying degree's, even if trying to be accurate as its nearly impossible for speakers to reproduce the original signal perfectly. many headphones and speakers are designed just for average listeners, so they will purposely alter the sound or EQ profile. the AT m50's are very popular, but also very well known as bass heavy. they are also closed-back headphones, which is good for keeping the audio from annoying others around you, but open-back headphones are usually preferred for mixing.
just starting out, you may be fine with a good pair of headphones and using the onboard realtek audio. if you want best results, you may want to look for an audio interface or headphone dac. using an external usb sound card/audio interface/dac keeps the electronic interference from the computer at a minimum. many regular consumer soundcards or headphone dac's are altered as well, in an attempt to make it sound "better", making them in-accurate.
you will want to get away from consumer products like asus, creative, beats, and look for pro audio brands like Sennheiser, AKG, Audio Technica, and Sony, to name a few. most of the pro audio brands do make consumer gear too, so its not as simple as picking a certain brand. for audio interfaces, Focusrite Scarlett models are popular, there is also presonus, m-audio and more. small portable headphone dac's are becoming more popular, but its rare to find any big pro audio name attached to them. still, some are reviewed as accurate/neutral. depending on your school, they might already have some audio interface connected to the computer to use with your headphones, or you could ask if its ok to bring in a heaphone dac or external audio interface.
Thanks for the reply. If I really do not need a sound card, that would be a blessing from a cost standpoint. I also want to point out that I also already use speakers which are poorly suited for pro audio (Logitech Z-5500 Digital). I have no plans to switch them out unless I have to, which is not at the present time. We are required to have our own headphones for video and audio classes in the Digital Arts department, so that is where my focus is for now. Switching the speaker setup is something to keep in mind for the future. Especially if I do more with video and audio work on the side even though it is not my specific concentration in the major. There are other components for my desktop PC that are higher priority such as a new graphics card, color calibration device, external drive (as required by the major,), potential internal storage upgrades, and a Wacom tablet.
The audio professor had the same suggestions with respect to audio brands. He can also give recommendations on makes and models within numerous price ranges. I'll do my own research and get his own recommendations. My main reason for writing this was whether I should buy a sound card or not.
Now if I did want to upgrade my speaker setup in the future (without breaking the bank), what do I do then to pump out sound to the speakers? My current setup is surround, if I can keep this kind of setup that would be fantastic as I use it for gaming. My guess is to get an affordable a/v receiver and hook it up to my video card via HDMI. I don't know how well that works with the a/v editing software however. Of course, I would still require passive speakers.
Now for my existing speaker setup, I would need to share the front speaker out on the back of the motherboard with the headphones. What is a good device to switch between my speakers and headphones? Could I just use the headphone jack on the control pod for the Logtechs?
there should be no harm in using headphones plugged into the logitech speakers headphones jack. if you have those logitech speakers connected to digital spdif from your computer, the sound might be even be cleaner. just make sure there is no settings in the logitech speakers that might change the audio signal, like some eq setting...
many of the basic usb audio interface devices also power speakers, but usually only 2-4 speakers, like someone might use for music mixing. if you were only using stereo for your a/v work, you might be fine with one of those devices and then switch the windows preferred audio device to your regular sound card and logitech speakers for gaming. if you needed surround sound for a/v work too, you would need one that has 6 (5.1) or 8 (7.1) channels and configure/route the outputs in your daw or other software to reproduce the surround sound channel layouts/mapping. using a home receiver with hdmi sound might work too, but i haven't set that up. i would guess it should be possible to map the 5.1 from your software to the hdmi audio output.
special music mixing speakers that are placed close to you are called "near field", where as if you had some big room setup with speakers placed away from you for surround sound theater, you might be using regular speakers. some home theater a/v receivers like from denon, also have sound calibration to make sure levels and eq are balanced and set properly. it uses a microphone, think of it kinda like video monitor calibration.