All of those. Latino doesn't have to do with Americas. It refers to the countries, and people of them that speak a language that derives from Latin. Like Hispanic, the U.S took the word to describe the people who spoke such languages in the Americas. The only difference is that it includes more than just the languages(and descendants) that are located on the Iberian peninsula, called by those who spoke latin Hispania, (Spanish,Portuguese), it includes the many descendants in South and Central America of Italians,French, and others who spoke Romance languages, all of which derived from Latin. So yes the Spanish are considered European, and yes they are considered Hispanic, and yes by those who are educated they are considered Latino, and if you want even more information most of the Spanish are Caucasian or White with some semitic influences, though Semites are Caucasian as well. Btw neither Hispanic, or Latino is a race classification. There are black, native, white, asian, and mixes between them who fall under this classification. Hispanic and Latino describe ethnic groups, and language groups that I have previously mentioned.
So here is how you would classify the spanish and people of Spanish decent.
Race: Caucasian/White(this includes those who aren't or very little mixed with Native or African)
Nationality: Spanish, those who have one or more grandparent/parent of whom were a citizen of Spain, but these descendants weren't born in Spain have the opportunity to get a citizenship much quicker if they chose to, as of now though their Nationality isn't Spanish, but of the country they were born, or a few other countries they might have claimed citizenship for in their life.
Edit: Some people are confused. Latino doesn't derive from Latin America, Latin America derives from Latino. Latino describes those who speak romance languages, or descend from those who speak romance languages.