Record karaoke on my PC

I am investigating the possibility of using my PC as a karaoke machine. This is for my wife, home use only, so the quality doesn't need to be spectacular...just decent. I am wanting to record the music/lyrics on the PC. Clearly, I will need to purchase a micophone but I have a couple of questions.

I would prefer a wireless mic but I don't know if I can get good quality...would I be better off going with a wired mic?

In order to achieve the sound I'm looking for, do I need to upgrade my sound card? Currently, I just have the stock sound card on my laptop.