So I am no pro but I recently set up a home karaoke system and I will tell you my thoughts.

First, in my experience normal TV/computer speakers are probably not going to be loud enough to be satisfying. If a loud singer is about the same volume as the amplified music... it just doesn't sound right. (I used my big-ass home theater speakers for a while because they can get loud enough... but I was always anxious listening for clipping and didn't want to damage them.)

So, I started using a powered standalone DJ style speaker. I happened to have it on hand for outdoor music and it works well for karaoke. What is important for you is that it is not only loud, but it has a small mixer built in.

This is what I have and it works ok for the money, but there are many such gadgets at all prices and quality levels.

https://smile.amazon.com/Rockville-Sistema-altavoces-8-pulgadas/dp/B00KL66FVG

So anyway, a powered DJ speaker WITH a 3 channel mixer built in (Music left + music right + mic), a microphone + XLR cable, a laptop computer with Karafun, and an audio cable from the computer to the speaker ... and you are in business.

For a mic, the Behringer XM8500 is $32. (oh man they used to be $23!) No it does not sound as good as a $100 Shure, but price is a factor here, and any sound system you have at your price point won't let you hear everything a better mic offers anyway.

This XLR cable will work fine.

If you get into it, you could then expand the system with an external mixer. This would give you more mic inputs and possibly other goodies like compression and vocal effects.

Ideally someone will be the "KJ" and run the karaoke app. The music you play may have different audio levels so it is helpful if someone can adjust the mixer levels as needed, too.

Sadly there is nothing you can buy an Amazon that can make you a good singer. :)