If you go for general taxation, you distribute the cost proportionally to income, making rich people pay more. Probably the ideal is a mix of both.
Taxing the carbon at the source is simply correctly pricing it, and because it makes it impossible to shift the externalities away from the producer it fixes the accounting problem that falsely makes fossil fuels appear cheap.
And obviously, you tax the fuel at the source, right when it comes out of the ground. Higher prices get passed down, changing behavior because the products externalities are priced correctly from the start.