Each privacy coin in the market has varying privacy requirements. It all comes down to what your needs and the level of privacy you require. But overall, Zcash and DASH comes in first as top privacy coins to have as they have quite sophisticated technology behind them.
Zcash transactions have the option to be protected in a way that both sender and receiver addresses, and the information that goes with the transaction are all made private using a technology called zk-SNARK, a technology that Ethereum has also started to utilize recently; zk-SNARK encrypts transactions between two parties making it a significantly safe coin to use. Zcash has also been performing well in the exchange market, and has a very decent valuation and volume which makes it a good pick for an investment for the long term. As it continue to get adopted in the market, you can expect it to grow in value in the near future possibly hitting a billion dollars in valuation. You may be intrigued with the fact that it also has low supply at around 2 million circulating with a relatively low production rate.
DASH has quite an amazing team behind it. As with any coin, the team members are an important indicator to whether the coin is worth an investment or not. To add to that, it has a rather effective marketing campaign that has made it widely adopted in the market. It is one of the leading coins driving cryptocurrency to mainstream adoption. Furthermore, DASH has considerably low sending fees which is something you might want to consider when looking at which privacy coins to have. DASH's wallet allows apps to be placed on the wallet making the need to go to websites or applications unnecessary. DASH enables the ability to conduct private transactions between apps through DASHpay system. Whatever purchases you want to make on the apps, you may do so incognito in the DASH wallet. In addition to that, DASH currently has a superb valuation if you're looking to invest in the long term. Its volume is sufficient enough to trade and invest with lower risks. Similar to Zcash, as DASH increasingly gets adopted in the market you can expect it to grow in value in the future. However, at its current value at new highs you should consider waiting for a pullback before investing.
Another coin to look at is Monero. It is however not a very good choice of a coin to mine as the payouts are not desirable. Recently, Monero has had a spike in value due to its listing on South Korean exchanges. Like Zcash and DASH, its supply in circulation is very low at 15 million. Monero is quite unique. It does what privacy coins are expected to do, that is to render all transactions untraceable and confidential but on top of that it is also currently in the works of implementing Kovri, which is their I2P anonymous network. An I2P anonymous network is what is being used in the Tor Browser and the deep web that gives users their anonymity. It also has a fitting amount of developers at 240 who have contributed to Monero including 30 core developers. If you're looking to invest in the coin, the situation is just the same as DASH. You might want to consider waiting for a major pullback before investing in Monero.
If you're looking for a great crypto miner to mine Monero, DASH and Zcash with, here's one you can check out. You can also start mining the above mentioned cryptocurrencies by downloading Minergate and start buying them at HitBTC.
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STOPHere is a good comparison of a few top privacy coins: https://www.reddit.com/r/monero/wiki/comparison. Also, the miner you suggested uses ASIC chips, and Monero is ASIC resistant, so it won't work very well for mining XMR.