What to use for error bars? When shall we use one standard deviation/error as opposed to a specified number of it, therefore producing a particular confidence interval?
And what would be the interpretation of these 2 different methods, i.e. significance for a difference, significance for a coefficient, etc?
 A: Basically, under the assumption of approximate normality there are certain well-defined regions based on standard deviation which have a fixed probability derived from the standard normal distribution: 
1) Mean plus/minus 1 standard deviation contains approximately 67% of the normally distributed data. 
2) Mean plus/minus 1.96 standard deviation contains exactly 95% of the normally distributed data which is the relation where the heuristic confidence region mean plus/minus 2 standard deviations comes from. 
3) Finally, mean plus/minus 3 standard deviations contains approximately 99.7% of the normally distributed data. 
So to come back to you question regarding interpretation, the location estimator plus/minus standard error, scenario 1), represents the "center of the data or area you expect to cover the value of your estimator".
Scenario 2) is typically used as the 95%  confidence interval for estimators. 
Scenario 3) can be used for outlier detection under approximate normality, as 3 out of 1000 points are to lie outside this interval. 
