How to see which transformation is the best
There are two main reasons people typically transform their data.  Either to help meet assumptions or to help boost predictive performance.


Help meet assumptions
In your case of a linear regression,  you have several assumptions that you have to meet including things like linearity and residuals have a constant variance and appear independent of each other.  Transforming your response can help make your relationship more linear and help with your residual assumptions, while a transformation on your predictors primarily helps with those residuals.  Typically if you are doing inference, you need normal residuals (or large sample size for CLT to kick in) which you can assess with a qq-plot or a test for normality, but if you are doing predictions you don't have to worry about this.  Trying a few popular transformations (sqrt, square, log) is a good idea, as is the Box-Cox transformation (on predictors) which basically finds a transformation that maximizes the normal likelihood function of the residuals.  The box-cox goes through several power transformations in a systematic manner, and it primarily used to make the residuals normal, though it can help the other issues too.
Improve predictive power
This is more of an open game, and I would be wary of over fitting.  See what works best and go with it (can be tough, might have to go with cross-validation if you're data isn't too big).
Your Case
Usually your x-axis for those plots is the fitted values (you can plot a glm object, not sure about lm, so run through most of your basic diagnostic plots). just with those plots its also tough to assess normality, which is typically done with a qq-plot or a hisotgram of the residuals.  It looks like your response variable new_users is a count; maybe a poisson model would be another option.  "best" transformation is the one that helps you meet your assumptions as noted in (1), its more of finding the transformation that makes you feel most confident that your assumptions are met.  If you are looking to increase performance, $R^2$ will help indicate a helpful transformation, but again be wary of overfitting.  The power transformations e.g.$(x^{1/3}), log(x+0.1), x^{2}$ are usually a good route to go.