Shiva and Quetzacotl are forced upon you when you leave Garden for the Fire Cavern. You can't miss them or Ifrit, so three is the minimum.
If you don't junction then the gameplay becomes very basic. You'll be using limit breaks on everything you see (Quistis' Degnerator is invaluable).
You can make things easier if you junction GFs for the purpose of learning refining abilities but don't junction any magic to stats. Then you can refine items and cards into stat-boosting items, enabling you to increase your stats while avoiding magic junctions.
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