Correlation of t-test or both?

I would appreciate some guidance.

I am tracking 300-odd occasionally used variables against a succession of dependent variables (one at a time) in order to see which one/s are possibly of importance - with a view to using or dropping those which are. n varies between 12 for some variables up to and 80 for one or two others. I'm using Excel 2019 and its functions.

At the moment I do two tests for this: whether the correlation squared is higher than 0.3 (that is r = 0.55); and a t-test, set at 5% - so if a variable has both an r squared of >0.3 and p < 0.05, I consider it needs being used or dropped (depending on which way it comes out).

So my question is, am I unnecessarily using two check when one will do?

And given there are >300 variables, should I be setting p at, say, <0.005 or some such.