My question is what steps could I take to use "my" mobile number (that I just ported to RW) as my Google Voice number
Instead of porting your number to RW, you could have ported it to GV, but that opportunity has since passed.
there is the GV android app where you can select what number to call from and display .
Republic Wireless and Google Voice are two separate services so it would be impossible to combine the two currently. You can either have your number be the public facing number on Google Voice which will forward to another number on Republic or you can have your number with Republic. The integration is currently only built for Sprint customers I think where they got together to build integration.
If you do want to port your number to Google Voice at some point, do note that you will have to go though some other third party such as T-Mobile as the systems running Republic and Google Voice do not allow direct transfers yet.