For the R Trigger connection you can solder to the rightmost pin of the ZIF connector on the motherboard (the one that connects the ribbon cable from the powerboard.) This is if you are looking at your motherboard in the way it would normally be oriented when using the PSP.
As for the ground wire, you should only need one for all of your buttons. The wire you have circled in the picture is a ground wire. There are lots of places on the powerboard and motherboard where you can connect the ground.