Alas, the first thing to say is "Don't record your classical guitar with a Xonar Essence STX". It's really not suitable for the job. The only input is an un balance 6.3mm jack socket which can do both line and mic level. Guess what? Any microphone even vaguely worth using will have a
balanced output on a 3 pin XLR connector. Most of the mics I'd recommend for classical guitar will be condensers which means they also require a source of phantom power.
So, what DO you need?
Well, as Guiitar Legend says, the first thing you need is a proper audio interface designed for recording, not watching videos and doing Skype calls. There are lots of USB interfaces on the market...GL has mentioned some but one you might specifically look at would be
the Focusrite Scarlett 2i2. It has two very good quality mic inputs (because a lot of the techniques for classical guitar record in stereo with two mics).
Microphones? You'll get as many answers as there are posts I suspect. My personal preference for classical guitar would be 1 or 2 small diaphragm condensers. Bearing in mind that you want a cheap as possible, have a look at the sE Electronics sE1A. I have some rather more expensive mics (AKG C451 and C391) but often fall back on the sE1A for guitar--I've recommended them a couple of times in here and the responders have been happy. As I mentioned, I like to work in stereo--you can get a matched pair of sE1A mics or you can start with just one and add a second if you decide you want to. The sE quality
control is good enough that I don't worry about matched pairs.
What else? Well, a mic stand with a boom arm...or two if you go stereo. Headphones so you can hear what you're recording as you do it. For mixing, ideally you'd have a set of monitor speakers. Again, there'll be lots of different suggestions.
Finally, your room. The
acoustics in the room you record in can have a big effect. Some people like a fairly dead acoustic (lots of soft stuff around, or proper acoustic treatment) while others like a nice sounding hall or cathedral effect with the mic a bit farther from the instrument. As I've bored people with before, when I was still working in TV, on more than one occasion I dragged vocalists or guitarists into a brick-walled stair well...not glamorous but it sounded really nice!