121 Domestic
1 hour before and after ETA: 3 miles vis and 2000' ceilings.

121 Supplemental
Must always file an alternate.

The required alternate whether is most likely going to be company specific.
In my case, if the airport has 1 nav aid, then you have to add 400' and 1 mile to the published mins; thus creating "derived" minimums. If the airport has 2 nav aids, then you have to add 200' and 1/2 mile to the published minimums.

Also, keep in mind that there are other alternates besides destination. There are also takeoff, wind, braking, and driftdown.