This is a pretty big business, but like everything big we need to start out small
First thing's first...
A computer (or laptop if you wanna go on the road)
You don't exactly need the greatest or latest model, but you need something a bit modern. This is great since it lets you record your voice, edit your recordings, is able to send your voice performance to anyone on the Web, and can operate and promote your voicing career. The type you get however is completely up to you. However, a computer isn't everything you need. You need some more pieces.
High Speed Internet Acess
Pretty small tidbit but it's useful nonetheless. Your sound files are gonna be big to send and receive so you'll need a fast computer to help.
The voice comes from your vocal chords vibrating in different ways. The microphone, in a way, turns the energy of our voice into another form of energy. Remember "energy can't be created or destroyed, only changed into another form of energy"? Basically that. In this case, it's transformed into mechanical energy then to electrical energy. Of course, you'll need to get a high-quality mic, one that fits you, since different mics can sound really different(yes, I realized the repetition). But there's something else.
Mics put out electricity, but not much. So the preamplifier, or preamp for short, is a device that boosts the output of the microphone to a presentable level. Like the microphone, the preamp's quality will effect your recordings. This usually comes in something called phantom power; power sent to mics needing it using the same microphone cable.
You'll need this to get pro-level sound in and out of the computer - sometimes called a sound card or A to D converter. The audio interface has a very important function; it turns the electricity the mic pumps out into a digital stream (1s and 0s basically) for the computer to recognize, turning it into what you record, hear, edit, and send out.
Speakers and Headphones
Once again, high quality ones. Not the built in ones found in computers. Make sure they can accurately expel the proper sound you want to hear, if not you'll end up with inferior recordings.