Bitcoin Gold is using algorithm called Equihash-BTG. This algorithm was used for the first time in Zcash and is now a more memory heavy and ASIC-resistant version 144,5
Virus warnings: expect warning when you download a miner. This is well known behavior. You can run the miner trough VirusTotal.
AMD video cards:
lolMiner for Windows 64bit and Linux 64bit
nVidia video cards:
EWBF’s CUDA Equihash miner
You can continue to Setting up the mining software »
The post above refers to available miners at the time BTG launched in 2017. After the Network Upgrade of July 2018, where the PoW algorithm was changed, that list of miners is no longer correct. Please refer to this list of miners which support BTG post-upgrade.