What kind of tires are recommended for this car?

To find out the standard tires on your car, go here:
http://www.vulcantire.com/tiresize.htm

Once you know the exact tires you have, you can navigate from there to check out different types.

prolly 16 or 17s

205/55-R16 if you don't have the sport package.  It depends on where you live and how you drive, but I like the Continental ContiProContact.  The provide long life, and reassuring handling in the dry and rain.
http://www.tirerack.com/tires/SelectTireSize.jsp?autoMake=BMW&autoModel=325i+Sedan&autoYear=2003&autoModClar=