I read that ancient Minhag before Shulchan-Aruch era was to put on Tefillin first then Tallit-Gadol. Is it true?
I am not aware of this custom. The Shulchan Aruch (25) writes that the Tallis is worn before the Tefillin, and this is based on the principle of Maalin BaKodesh – the kedushah of Tefillin is greater than that of the Tallis.
It stands to reason that this was also the prevalent custom, since otherwise this will have found mention in the commentaries around the Shulchan Aruch and by other authorities of the time.