There actually are a few degrees of "love" in Czech. If you are attracted to someone, perhaps you "like" them: "Líbíš se mi." If you're in a serious relation with someone, you might say "Mám tě rád(a)" (use the variant 'ráda' if you're a woman), which is typically translated as love, but not as serious a love as the third variant. This second variant is most often used among boyfriend/girlfriend, siblings, parent-to-child and vice-versa. If you're totally committed to someone, you might say "Miluju tě." This third variant is not used as much (typically between spouses), although its use is apparently becoming more commonplace.
I get the impression that it is not as common for Czechs to say "I love You." (as it is in America.) Is this a fair assumption? In relationships, does the man always say I love you first, or the woman? (Or is it insignificant.) Are men less verbal there?
Yes, that's true. When you say "Miluji tě", you better mean it. And it is very rarely used in parent - child etc. relatonships. Very strong expression, used only by lovers and on special occasions, as I see it Generally, talking out ones emotions is quite unusuall. The classical Hollywood movie scene - "I love you, son. - I love you too." does not seem to fit in Czech life.