Which B coefficient can I used to interpret the unit of effect of independent variable to dependent variable for those variables significant in multivariate linear regression can I used the standardized or unstandardized B coefficient
If your aim is to only measure the effect of the independant variable upon the dependant one, the unstandardized estimate is enough.
In the case you also want to allow for direct comparisons between different predictors you could add the standardized estimate as well.
From my experience the unstandardized estimate is much more commonly used, however this is field specific and it may vary.
I think it is more worthwhile to consider standard beta coefficient when multiple linear regression will be performed.
Unstandardized coefficients are usually easier to interpret since they often refer to meanigful measurment units such as as age, height, wage etc. Hence, model interpretation is usually "straight forward", e.g. wage is increasing at $500 per decade, women earn $200 less than men etc. While I agree with Stefanos that direct comparisons between different predictors can be easily done by using standardized coefficients, you may want to consider taking your unstandardized estimates a step further by exploring marginal effects, i.e. show different outcomes over a range of relevant values of some independent varialbe(s) while adjusting for the remaining independent variables (e.g. at their mean value). The latter can be done quite nicely with graphs and can facilitate your understanding of complex model, espcially if they include interaction terms.
Standardized coefficients give the illusion of placing variables on a common scale, but do not actually do so. Unstandardised coefficients should generally be preferred for most purposes - especially interpretation. There are various factors that influence variability that don't change the magnitude of an effect and hence influence beta but not b.
Article Standardized or simple effect size: What should be reported?
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