Microphone suggestions or software to avoid background noise in audio
Your most critical need is going to be a professional low noise analog to digital converter and pre-amp with a decent quality microphone to go with it.  There are a few options you can pursue for this depending on your interests.

Since you are currently working with a computer directly, you could go for any of a number of professional audio capture devices with XLR and phantom power capabilities, such as the X2U adapter from Shure that you were talking about or a device like an MAudio audio interface unit.  

Since these only provide inputs you would also need a microphone.  Depending on how close you mind the mic being, something as simple as an SM58 would produce nice clean audio for you, this has the added advantage of being usable really close to your mouth and focusing the pickup in a cardioid pattern that mostly picks up stuff in front of the microphone, thus it will pick up less background noise.

Alternately, you could use a condenser mic or shotgun mic that could be placed further away, however a condenser mic would pick up more of the room sound and a shotgun mic would require careful aiming in order to make sure it picks you up and not the room.  A Lapel mic or LAV is also an option.  A lapel mic is a type of condenser that can clip to your shirt and therefore pick up a little less noise, but will still be in the shot, though it is less obvious than a dynamic mic like an SM58.

Yet another option to get additional flexibility is to go with a device like an H4n recorder.  This is what I use for my video work.  It is a stand alone recorder which can also be used as an audio interface for the PC and also has built in stereo condenser mics.  The device runs a little bit more expensive than an audio interface, but is normally a bit cheaper than an interface and a condenser mic pair.  It also can be used away from a computer for any project.

Additionally, the H4n includes XLR and 1/4" inputs so that it can be used with any of the mics you could use with an audio interface if you later decide to upgrade or change to a different kind of microphone for a particular recording task.