What should you wear for davening?
Today's daf (Shabbas 10) has the din that a person needs to be dressed properly for davening. The gemara states that a person cannot daven without a gartel (belt) based on the pasuk of הכון לקראת אלוקיך. The poskim explain that this means that a person needs to be fully dressed and ready to speak to the king.
RHS told over a funny story from R' Schwab. He was going to daven mincha and there was a businessman wearing a suit. The man had forgotten his gartel, so he took his tie off and used it as a gartel. R' Schwab commented that what the man did was incorrect. Nowadays, a gartel is a minhag, it is not part of a person's dress. However, a tie is an integral part of a person's dress (for businessman) and for many people if they are not wearing a tie they are not fully dressed. Therefore, the man would have been better off leaving the tie on and not davening with a gartel as the gartel is stam a minhag while the tie could be min hadin.
RHS mentioned a story about RYBS (in Nefesh Harav) that at some point the Rav stopped wearing a jacket for shacharis during the week. One of the talmidim asked him why? He explained that he started wearing R' Chaim's old tefillin, and the batim were very large so he couldn't put his arm with the tefillin on them into the sleeve. So what? He said that no one would walk around in the street or to meet an important person with their jacket on like that (one arm not in) and therefore he thought that it was more kavod not to wear the jacket at all.
In YU and other places, many people have a minhag to wear a jacket for davening. However, they wear any old light jacket (windbreaker). This minhag seems very difficult, the idea of wearing a jacket is this din of being fully dressed, wearing an ordinary light jacket would not seem to fulfill this din.