FAA take off minimums

[che ci dò che ci dò!]

Guys,
I'm studying for the FAA Atpl and I'm getting confused with take off minimums as for CFS 121.637 and 91.175.
The latter states that, if T.O. minimums are not prescribed under part 97, for two engines aircrafts under 121, 125, 129, 135, the minimum T.O. visibility is one mile.
CFS 121.637 states that, when operating under part 121, in the absence of T.O. minimums, the following applies: 800-2, 900-1 1/2, 1000-1
When operating under part 121, which of the two above should I apply when there's no prescribed take off minimum? And when should I apply 800-2 rather than 900-1 or 1000-1?
My apology but I'm new to this kind of stuff.

[MarkerInbound]

Domestic and Flag air carriers have the airports they are approved to fly into listed in their Operations Specifications. 121.637 is for when, for some reason, they end up at an airport not listed in the OpsSpecs. There is normally no ceiling requirement in FAA land. However in this case there is. So if we were at an unlisted airport, in order to use the minimum visibility allowed per 91.175(c), we would also have to have a 1000 foot ceiling. If the ceiling was 800 feet we'd need 2 miles vis. If the ceiling was less than 800 feet, per 121.637 we're stuck there.

The ATP knowledge test covers the regulations as published for everyone. In the real world most airline's OpsSpecs get paragragh C078 which covers lower than standard TO minimums and, depending on training, airplane equipment, runway lights and markings, and the number of RVR sensors, can get you down to 300/300/300 (75m/75m/75m).