For simple recording with effects, if you don't want to spend any money, download the free source program
Audacity. It isn't fancy, doesn't have all the features of other recording programs, but the flip side is it does have effects that can be applied to a recording and has a short learning curve.
Set Audacity to record stereo mix from your computer soundboard (probably the default) and then set your mic. Then I open up my program to play the music (I use Windows Media Player or Musicmatch Jukebox and Audacity at the same time. If you need lyrics, pull up your browser and do a search for the lyrics for the song you want to do. I set my levels then hit record on Audacity then play on the music player. Then I click on the browser for the lyrics and start singing. Once recorded I check it then you can select all and add echo or do any of the other effects that are in the effects menu. Keep in mind the effects menu doesn't work unless you select all.
It's not feature filled like other programs but it does have things you can use, takes up less hard drive space, there are many internet sites with help for it, the cost is right, and it is simple to learn and use, especially for a beginner.
Hope this helps.
ZAP!