From what I have read Geta was the favoured son of his mother, Julia Domna, in whose arms he died.

As for the army, surely all Geta had to do to ensure the popularity of the soldiers was a large pay-off and a substantial pay rise, two things that Caracalla did following the murder of his brother. Money was not a problem for as Herodian states Severus had died "bequeathing to them (Caracalla and Geta) greater wealth than any previous emperor and an invincible army"