Microphone
It doesn't really matter what microphone you use to record with. The two most important technical choices you should make are the room you record in and the microphone placement and position. If you are in a room that has acoustic properties not that dissimilar to a bath room then move the microphone around to an area of the room that sounds better. Lots of home music producers open the wardrobe in their bedrooms and place the microphone in there.
Floors
If you record in a room with wooden floors then you should get the vocalists to record with their shoes off, or at least put a small rug down under their feet. Some singers tap their feet when recording. Toe tapping can be loud on wooden floors thus being picked up through the mic. It's easier to eliminate problems like these at the start rather than later on.
Signal Level
Always check if your recording level into your computer is too hot. You'll see this by the track you are recording to. Usually this will show red, red is bad, red is ugly, red is redo. Try to avoid recording anything that hits red. Red is digital clipping which results in an unpleasant distortion sound which cannot be fixed later. Try to set your record signals to half the level of distortion. This gives you something called headroom. Headroom is your friend. It gives you space for louder signals in the performance and also provides room to turn audio levels up into. Without headroom the only place is red... redo.
Headphones
Get yourself a decent set of headphones. Avoid ear buds and invest in a good set of over ear headphones.These help minimise bleed from your music as it plays back in recording.It also gives the vocalist something more comfortable to wear.
Performance
As you are recording at home you can take your time, you are not in a professional recording studio paying by the hour. Don't rush the performances or the setup time.Take time in arranging melodies and recording demo vocals so that you can hear your ideas before committing melodies to the production stage. Be professional in the approach to recording and ignore the fact you're at home. At the end of the day it's all about performance, without a great performance why record anything.