Is there a preference which side of the Aaron one approaches from when he goes to do Pesicha?
There is no preference which side to go to the aron to open it. However when the torah is taken to and from the bimah, it should be done while walking to the right. Meaning that if the aron hakodesh is facing east, you should walk to the binah towards the north, and when returning the sefer torah we go from the bimah to the aron hakodesh towards the south. Additionally when going to the bimah to get an Aliya if both ways are the same distance we go toward the right.
Shulchan Aruch 141-7, M:B 141-25.