Which measure to check in analysis (p-values or $R^2$)? In an analysis e.g. OLS regression which measure would you look at?

$R^2$, $adjusted-R^2$ or $p-value$?

How would you consider a regression with p-values >0.15 but with an $R^2$ of 40%?
In general in economics, what have you seen?
R-squareds and p-values give different information. For example, suppose that you regress birth weight on mother's smoking. The p-value tells us whether the association is indeed nonzero (in the statistical sense), and the R-squared tells us how much of variation in birth weight is explained by mother's smoking. 

p-value > .15 and R-squared 40% would mean that (1) we can't say that the association is nonzero (2) but the explanatory power for the given sample is quite large. The two neither reinforce each other nor are contradictory.