Te amo is what people who are in love say to each other. Te quiero is like saying you are very fond of that person. You have love for someone, but not necessarily in a romantic way. In Spanish, people rarely say te amo. Although it is used a lot in telenovelas, soap operas, and the like.
I should also mention here "me gusta". I know in English you say I like him very much or I like her and everyone understands what you mean. In Spanish, when you say " Me gusta mucho fulano" it implies attraction, sexual attraction. When a man declares " A m? me gustan las mujeres" he is saying he is attracted to women, not men, for example.
If someone asks you ?Te gusta ese hombre? if you are a woman the question means "Are you attracted to that man?
If you simply want to say you like someone in a non sexual way, you say: Me cae muy bien. Me cae bien tu hermano, etc. Of course, you may also say "Me gusta como habla" I like the way he talks, and then it is ok to use me gusta. When you are describing a quality a person has, then it is ok to use me gusta.
Me gustan las personas honradas. I like honest- upright- people.