It`s really either one or the other. Research into mining not only allows you to pull ore quicker, but it produces more minerals per turn. It also doesn`t matter if you have any mining infrastructure on your colonies at all. Mining is easy and cheap since you don`t really have a need for infrastructure. You could have a 10 land C1 and it would produce as much mineral as a 4000 C1. Saves on population costs to go as low as possible and it makes exploring a snap. So if you`re going A.Miner, get 5 research into industry for the +5 mining mission bonus (save it for later, don`t use it right away) and focus everything else into Mining. When you hit the 2500 turn research mark, complete the mission and save yourself a LOT of time and you`ll make yourself a lot of money.
Tax Miners are really just rewardable Guardians without the good ships, save for Lictor. Get the biggest colonies you can and don`t forget the borders. Pay for your food and keep the population and loyalty count as high as possible. No other infrastructure needed. Ever. Missions for that one are optional, IMO. +Loyalty rewards are alright, but the mining bonus just cuts what research you could have in Housing.