Being able to grow a successful goatee is usually not usually going to be a thing you have much control over, unfortunately. The success or other wise will depend on such factors as: hair colour & beard colour (not always the same...), density of hair follicles, shape of face etc. The best way, in fact the only way to find out what you'll look like is to grow one. Or draw on your face with felt pen.
There is one piece of crucial advice I would give, however, and this is fairly important. Don't start your goatee from scratch, ie a cleanly shaven face. The best start is to not shave at all for at least a week, preferably around 10 days. Obviously, doing this during a holiday is best if you work at a job where looking clean shaven is required. Ending the growing period on a weekend is probably best if you plan to do this during a non-holiday period.
Having a substantial amount of stubble on your face will now show you what you have to work with. If it's patchy or thin or uneven or whatever, it might not be a good idea to keep a goatee, but with this method, you'll know what it will look like anyway. That's the beauty!
Picking a simple area on your chin and upper lip (an accompanying moustache is of course optional, especially among jazz musicians and beatniks...)to keep - nothing fancy, at least for now! - shave the non-required stubble away - a new, sharp razor blade will help you avoid horrible razor burn, obviously. Ensure you see the goatee from the side, as well as from in front, it may benefit from a sloped, curved or straight vertical shape. This will depend on the shape of your chin.
Once you have your proto-goatee, then take a break. Come back in half an hour or so to re-check it in the mirror. This will give you a degree of objectivity needed in deciding to keep it or not. If it looks alright, and matches your face, go for it. It may, of course look a little odd due to being a new thing on your face, but don't let that put you off.
Also, don't worry about the 'itchy' phase of beard growing - it soon passes in a week or so, once your skin's used to it.