Which of this group of animals made the first transition from aquatic to the terrestrial mode of life?
The most famous animals of late Devonian era, that made a transition from aquatic to terrestrial mode of life, are Ichthyostega and Tiktaalik. Some other animals can also be mentioned. All those vertebrates can be qualified as representatives of one of next five groups: Sarcopterygian fishes, prototetrapods, aquatic tetrapods, true tetrapods, and terrestrial tetrapods. Simply, all of them are specific lobe-finned fish (they are part of bony fish group) that developed limbs and lungs. Also they changed their mode of reproduction from larval development to metamorphosis and feeding mechanism from suction feeding to biting.
References
Long, JA; Gordon, MS (September–October 2004). "The Greatest Step in Vertebrate History: A Paleobiological Review of the Fish-Tetrapod Transition". Physiological and Biochemical Zoology. 77 (5): 700–719. doi:10.1086/425183.
Clack, Jennifer A. (2012). Gaining ground : the origin and evolution of tetrapods (2nd ed.). Bloomington: Indiana University Press.
https://en.wikipedia.org/wiki/Vertebrate_land_invasion