Would the Spanish from these lessons only be useful only in Latin America (like Mexico, Southern US), or both Latin America and Spain?
You can get by with it just fine in Spain - people will understand what you mean - but there will be a lot of words where they'll say, "What? Oh, we don't say that, we say this!" It's a little like American English vs. British English... you can have a conversation just fine, but individual words will get that 'huh?' reaction (like boot/trunk, pants/underwear, biscuit/cookie, crisps/chips etc). My favorite Spanish teacher in high school took about 8 years of Latin American Spanish in school and then did a two year stint studying abroad in Spain, and she got on fine (and enjoyed herself immensely) even though, as she told us, "they used all kinds of words I'd never heard before!" She advised us that if we ever went to Spain, we should remember the usefulness of describing things, so that if we used a word that Spaniards weren't familiar with, we could get our point across enough for them to give us the local word - e.g. "How do you say that food that's meat between two pieces of bread?" if we needed the word for "sandwich". It's a trick that beginners use a lot, but "Cómo se dice ...?" is just as useful when you've hit a dialectical difference, which was her point in telling us that story.
Also, most areas of Spain pronounce their Ss differently (closer to a th, sometimes called the Spanish lisp), so that's something to be aware of. You can read more about that here, if you're interested.