Cubase is a very versatile editing & mastering software. One of the most popular out on the market today. Just about any feature you could possibly need to create top quality home recordings are included.
One option I find very user friendly is a free software called Audacity. Your probably familiar with the name. It doesn't have all the sophisticated mechanics of Cubase and some of the other software but it can get the job done. If the music is good to begin with Audacity can help to really shape and polish the song into a finished product.