The question contains a common confusion. The Visigoths (Western Goths)—not the Ostrogoths (Eastern Goths)—established the kingdom in Spain.
The Ostrogoths established their kingdom in Italy under Theodoric the Great (493), ruling from Ravenna. Justinian's reconquest (535-554) destroyed it. They never ruled Spain.
Both are "Goths" (Germanic peoples from Gothic culture). Both had kingdoms in former Roman territory simultaneously (6th century). Both interacted with Byzantium. But geographically distinct: Visigoths = Iberia (+ Gaul), Ostrogoths = Italy.
Visigothic contributions: Catholic unification, legal code influencing medieval Spain, architectural style (horseshoe arch), preservation of Roman administration. The "Reconquista" narrative later claimed Visigothic continuity.