If I had to choose would I be better off with an AMD RX 580 4GB or a Nvidia GTX 1060 3GB
I hear that AMD are slightly more efficient at mining but are more prone to overheating which isn't good.
Also, could I still use the computer for light tasks like talking to people on facebook or internet surfing while mining?
Awesome! Can I keep it on mining at night while I sleep?
Of course you can! And if the day in the Claymore to stop mining it is also possible to watch films and play games, and then again to start mining.
Nice, so I'll probably start with Etherium since that's booming right now but do you guys recommend any other alt currencies that will work on an RX580 as well?
Check out whattomine.com and plug in your card, it will tell you what is most profitable to mine currently, over the last 24h, last week, etc based on profitability, difficulty, and power usage. Eth might not always be the best ethhash coin to mine.