1) My recommendation especially to get the best overall deal would be to buy used. I would recommend getting yourself an Ibanez. Check out RG's. I would say to stay away from the cheap GIO series though. Buying a used RG would allow you to get a really good quality guitar for that price range. Ibanez are some of the best guitars I have played for the price.

2)Now I just mentioned how buying used would save you money but with you being left handed it might be problematic. If you could find a used left hander though it would actual be cheaper (from my experience) due to a shortage of demand for left handers. Shops usually have a hard time selling them. My suggestion would be to call local guitar shops and ask.

3)Are there specific guitars for those genres? Well, there are guitars that are definitely marketed towards metalheads but any guitar would work (see Iron Maiden's Strats). Examples would be anything Jackson, Ibanez RG's and Xiphos, along with Deans and BC Rich. Now granted some sound better than others but this usually has more to do with your pickups and amp. Common pickups to have now days are the EMG active series. Also Dimarzio offers many great passive pickup options (these are what I use)

4) If you find a guitar/amp you are interested in check out reviews! If it is a popular item chances are you will find out exactly what you will be getting before you buy. Just start doing research at music sites online such as sweetwater/musiciansfriend etc.

I had your exact mindset when I started playing. I started rocking Metallica riffs right out of the gate without touching an acoustic for about 3 years after. There is nothing wrong with that. Play what you want to play and the rest will come later. If you bore yourself right away then you will never play.