Note that all of these are now significant individually. The r-square is about the same as we got with all the variables in, but we have removed extraneous variables. Backwards is a very good technique for this particular situation. Here are some questions that I didn't ask, but should have. If you have some time, I recommend experimenting a bit to see that you can understand the output from these various methods.
Beta is the standardized regression coefficient.
It is an indication of the level of individual influence on the regression variate. If there is multicollinearity, beta may be very different from the simple correlation coefficient. You can't really tell a thing from the other coefficients. Make a plot of the residuals. The analysis does seem to have met the assumptions fairly well.