Recitiation of Ashrei as a special merit [Segulah] for The "World to Come": Berachot 4b, MYT Berachot 1:6:6
Recitiation 3 Times a Day: Berachot 4b (Note that some Rishonim had a different edition)
Reason for the Thrice-Daily Repetition: R. Berachot 4b "Shalosh"
Special characteristics of Ashrei: Berachot 4b
Starting The Afternoon Service with Ashrei: Rosh Berachot 1:6