On weekdays, people come to services in their workday clothes. Shabbat is a little more formal.
On weekdays (Sunday through Friday), while you’re there, you’ve got a great opportunity to score another mitzvah: ask the rabbi for help wrapping in tallit and tefillin. These are worn for the morning prayers, but if you missed the morning, you can still put on the tefillin in the afternoon. See our tefillin wizard for more info.
As much as saying the Kaddish can do for the soul of the deceased, that tallit and tefillin can carry it even higher. At first, it may seem a little awkward, but with time it starts to feel just right. You might want to ask your rabbi if he can help you purchase your own set of tallit and tefillin.