The Iberian Peninsula was inhabited long before the Romans occupied it, and the PaleoHispanic people's had lived in northern and Western Iberia since the Stone Age (35-40,000 BCE). Modern Spanish are descended from a rich mixture of Roman, Visigoth, Vandal, Muslim, Celtic and the PaleoHispanic, but all of these ratios are different depending on where you go in Spain to look at the population. Portugal is rich in Muslim and Roman influence because of the importance of the region for trade, whereas the North in places like Basque remained pretty culturally and linguistically solid even through Roman and Muslim occupation. Besides that, in the South East there's even influence from the Greeks and Phoenecians. So ultimately the peoples of Spain have many different origins, so it really depends on where you want to focus on.