non normality in multiple linear regression I am trying to figure out which regressors to include in my model and assess my model's adequacy. I know my data is skewed. My question is: 
should I do transformation first or model selection first?

When I fit the full model, i seem to have non-constant variance of the error and also deviance from normality. I have applied a log transformation of the response variable: This removes the non constancy of the error but adds a curvature in the qqplot. I would like to use my model for frequenstist prediction and baysian prediction. I am aware thet deviations from normality can cause inacurrate prediction results.  What should I do about the non-normality?
I have conducted a Shapiro test- it has been rejected, therefore i conclude that there is enough evidence that the data are not normal.

EDIT: My sample size is 250. Can i ignore the non-normality because I have many observations?
The response variable is Salary: 

EDIT 2: Added Variable Plots (as kindly suggested by Whuber)
As far as I know Added variable plots are used to detect disproportionate influence of observations. I do not see anything suspicious here that would explain or suggest the indicated bimodality. 
Am I missing something here? 

 A: Okay, a few things.
1) I always advise against using tests for normality. They answer a question you already know the answer to, i.e. "Is your data normal?" (The answer is no because nothing is normal) vs the question "Is the lack of normality going to be a problem?" which is the question you should be interested in.
2) The assumption of normality is not so much about the predictive performance, but rather the correctness of the inference you would perform (hypothesis tests and confidence intervals). 
3) Some deviation from normality is okay, because we have asymptotics that drive test statistics to normality.
4) You QQ-plot does not appear to be severely not normal (although there might be some bimodality in your residuals. You may want to check if there is an omitted variable or something). As another commenter stated, the normality is the one that can kind of fail (can have mild - moderate deviations from it).
5) So to answer your question
(i) Yes, you do the log transform (or some other transformation) first.
(ii) Once you transform your variable the nonnormality EDIT may be worth looking to see why the residuals seem to be in two distinct clusters.
A: Note: Linear regression does not have assumptions on response variable to be normally distributed. Instead, it has assumptions on residual needs to be normally distributed (See Gauss-Markov theorem). In addition, this assumption is the "least important one", i.e., can be violated and the model will work "fine".
They are different, one is on marginal distribution and another is the conditional distribution. An detailed example can be found here: Why linear regression has assumption on residual but generalized linear model has assumptions on response?
A: I wouldn't worry about normality, at least, at this stage of your analysis. Try using log transformation on the dependent variable. Salary's a good candidate for log-transform. This removes skewness, then you'll be good to continue analysis.
