Not sure what kind of budget you have but I'd look at getting a vocal/interface bundle.
The basic kit I'd go for is:
An audio interface
Some decent headphones
A mic + cable + stand + pop shield
this might be a useful starting point:http://www.dv247.com/computer-hardware/focusrite-2i2-and-se-x1-recording-b
You'd just need some headphones and recording software, some
of the cheaper options are reaper or logic express. There are a range of free ones too,
I'm sure somebody else can help you out here.
You might also consider a vocal
shield like the se electronics reflection filter,this will help if the room you record in
has poor acoustics.