As far as I can tell, the $1200 per person will be coming based on 2018/2019 tax returns. Anyone who made under 75k individual or 150k married will be getting the full amount with it being a lesser amount for people who made over that up until about 100k/200k where it will decrease to nothing. I think the formula is for every $100 over 75k you made, they reduce the amount by $5. There's also additional money for children dependents, but I paid less attention to that as I have none.
Theoretically if you fall somewhere in the "above 75k/150k" area, you might be able to game the system a little by either not filing your 2019 returns until after you get the check if you did better in 2019 than 2018, or making sure you file now if you did worse in 2019.
As far as I can tell there is no lower limit on the $1200 like there has been on some previous programs, all you need to do is have filed your taxes for either 2018 or 2019. They say they're attempting to figure out something to offer to people who have not filed taxes, but I have not heard anything specific.
Most clear info I can find at the moment:
https://www.wpri.com/health/coronavirus/qa-heres-how-your-federal-coronavirus-relief-check-will-work/EDIT: Apparently the full amount will be based on your 2020 income though, where if you miss out on some by doing better in 2018/2019 than you did in 2020, it will come back as a rebate on your 2020 taxes. But it says if they pay you too much because you did better in 2020 than previously, you wouldn't have to pay it back.