What is the difference between chooosing a linear curve as opposed to linear thru zero? Also what does it mean to do a linear regression of your results? Is that your calibration curve?

A linear curve is just that, usually with a non-zero intercept. A "linear through zero" curve simply forces the x and y-intercepts to be zero, approximating the rest of your curve as closely as possible. In most cases, "linear through zero" gives results very close to the unmanipulated data.
Linear regression is the process, classically by the least-squares method by which your calibration data is reduced to a calibration curve.

Since no calibration line truly goes thru zero it is best not to force the line thru zero. A non zero intercept on the horizontal axis could mean problems with the blank;thri the x axis detection limit problems.

I have found that the curve-fitting model (for 3 or more points for assays and impurity methods) that has worked consistently well for me is:

linear fit
ignore origin
equal weighting for assays
quadratic weighting for impurities

These calibration model settings tend to give the best correlation coefficient (r) values as well as minimum residuals (difference between actual y-value and expectation value) for each of the calibration levels.

Using calculations from a text such as Miller and Miller, 3rd edition, you can usually demonstrate that the intercept confidence interval always includes zero, unless something strange is going on. I have seen non-zero intercepts when decomposition is occurring in GC or when on-column decomposition occurs in LC.