The
Shure SM58 is a great beginner vocal mic. The condenser in the OP would work well too, if you're just doing vocals.
Do I need anything other then a computer with an audio jack and a USB slot or do I need an audio dock or whatever the forget they're called?
An interface is pretty much necessary when recording with actual microphones. I use a
Behringer Q802USB for my stuff, but a
302USB will work just as well.
Also would I need a stand for this?
It helps a lot to have a
shockmount and stand because it eliminates all extraneous handling noises. While I'm at it, I'd recommend getting a
pop filter so as to keep your plosives out (and a stand is needed to mount this).
Would it be worth just getting this https://www.amazon.ca/HyperX-Cloud-Gaming-Headset-PS4/dp/B00SAYCVTQ
Instead of a microphone and if so how big is the mic quality difference?
I can't say for sure but my experience with mics on headsets is that in general they have a much, much smaller frequency range and the resulting audio is always tinny and thin with no bass or mids. An actual, professional microphone is going to be much better for pro-audio recording.
Also, keep in mind with audio equipment you will save a lot of money if you buy used. SM58s pretty much always go for under a $100 used, and the same with stands. Don't buy a used pop filter though, unless you want mouth herpes or something lol