What doctrines teach that people are inherently good or bad? Are we "basically sinful" or "basically good" (are we born fundamentally sinful, or are we born holy but then "fall to temptation?).

What I really want are the names of the doctrines associated with that age-old question - not the answers themselves.

I seem to think that it's a "Lutheran vs Methodist" argument, am I right? (But...  They seem to focus more on day-to-day living, not the "born sinful" part).
The doctrine that says that we are all born fundamentally sinful is called total depravity.  It is held by the vast majority of protestants - Lutheran and Methodist alike.  This is one area of agreement between Calvinists and Arminians.

Although not quite teaching that we are "basically good", one step closer to that is limited depravity.  It is the belief that we are born sinful, yet with enough good in us to accept Christ.  This may be similar to the Catholic view, although I am sure there are some finer points in which it differs (perhaps a Catholic can comment on this).  I am not aware of any other mainstream branches of Christianity that hold this view.

Mormonism does teach that human beings are not "basically sinful" (though they do not claim that human beings are "basically good"), as a part of their restored doctrine of atonement:


  According to Christ’s original doctrine as restored through Joseph Smith, the Fall made both possible and necessary the Savior’s atoning for our sins. Human nature is neither inherently evil nor inherently good. We become evil or good based on interaction between the Lord’s influence and the choices we make—choices unavailable in the garden before Adam and Eve fell and only made possible because of the Savior’s atonement.