Need help choosing tires.

First car having on my own so it's difficult to find out what tires to get after they're worn off. I don't want to got to the dealership and pay $225 for each tire. Is there any ways I can buy cheaper tires? If so, could I just bring my car to any shop for the installation of the tires?

I have a 330xi 06 4D btw

What size tires do you have? We may have better pricing than many local shops.