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That depends on what you want and how much electricity costs at your place. AMD cards are generally beter at mining many different coins, while GeForce cards are more expensive, have slightly better hashrate but can't mine as many different coins. If you use mining software like NiceHash, whatever coin you're mining can be converted into BTC at a small premium as well. In general check two things that are often overlooked: check what power unit is built in and make sure it has all types of protection against power surges and make sure its capacity is well over the amount used by the cards, mother board and processor combined. I'm going for a rig with 6 AMD RX5700XT cards this time and a 1500 watt Corsair power unit with an 80+ Titanium rating. According to whattomine.com that'll yield us something around 25 euros per day. The rig is built as a closed stackable unit with 6 fans and certainly isn't the most cost effective one on sale; it has an ROI of 256 days, but it's silent, very well cooled and uses only premium components. If you look around though there are much cheaper solutions available for beginning miners; just watch the video and you'll see what I mean, it's how I started the first time :-)

I live in NZ and the power is quite expensive, somewhere around the $0.30 Kw/hr mark. I'd love to set up a rig when I eventually have my own place with some solar panels. Thanks a lot for your comprehensive answer.