Tany, few questions for ya..
1) Can u sing w/o looking at the lyrics? If yes, u can connect w/o TV. However, i doubt normal comp spkr will sound good for singing..Dats my 2 cents..
2) Wat r u using to record? Cassette recorder, md, cd recorder????
3) Imo, mixer is essential in recording as it;
- provide a platform where multiple inputs can be connected
- balance the volume of ur music, vocal or any other instruments so that no one is louder than the other..
- can do some basic eq to the sound to ur liking(example, if u have a thin voice, u can boost the "lo" and probably some "mid" to make your voice sound more "thick")
4) Can provide the model no of that US$99 Yammy portable PA?
Cheers