Growth of debt: exponential, logarithmic, or linear? If I have increasing debt that I don't intent to pay off for a really long time, how would I prefer to have it grow? Exponentially, logarithmically, or linearly?

As Yuriy S says, you should choose the logarithmic, since it will (eventually) be overtaken by the two others no matter how you tweak the parameters. The exponential function is by far the fastest growing of the three, and it is sadly also the one most (all) loans use. See this question about comparing growth rates.

Here are the three functions plotted, with all parameters set to $1$ (note that the differences only become more clear the bigger $x$ becomes):

![enter image description here](