The carbon tax should be set at a rate that offsets any cost the energy producers are externalizing to the rest of us. I think the best choice would be directing the money into energy research (efficiency or clean production), an tax credit would fine in principle but would likely end up mostly going to large corporations, in no case should it go into the general fund. With the rate at that level it shouldn't be excessively burdensome and consumers will make rational choices on how to adapt.
The current best estimate of this cost is $40/ton in 2015 dollars. At a rough estimate this would increase the cost of Gasoline about $0.18 a gallon for an average car. Obviously it would have a variety of follow on effects for energy prices and the price of goods though industry would scramble to implement newly positive NPV projects that increased energy efficiency or switch fuel sources as appropriate so once things settled down it wouldn't really be that big a deal. Perhaps we might all be about 2% worse off compared to now, which sucks but is better than letting things get out of control and then doing crazy things later.