First off, Latin is NOT a dead language. :-)
Second, I must commend you on picking goals before starting a program. So often, we start up some curriculum or project, without really understanding what the end goals are. Obviously, this makes it really hard to assess how we are doing towards those goals.
Now, there are a lot of valid reasons for learning Latin. First, it has been shown that students who student Latin have much higher SAT scores than those who do not. (post hoc ergo propter hoc, and all that) However, this is not a good reason to study Latin unto itself. If you just want improved standardized test scores, it is more time-effective to just focus on test prep. (Not nearly so interesting, but nonetheless more effective)
Also, Latin scholars tend to have "better" (or more) vocabulary than those who do not study Latin. However, if you just want to improve your vocabulary, memorizing word lists is probably the best way to do that. (Again, not nearly as fun as learning Latin, IMHO). Moreover, many people (including those who make standardized tests) confuse large vocabularies with better intelligence or better writing ability. Believe you me, there is nothing so tedious as a dull writer with a flair for throwing around obtuse words.
Studying Latin will improve your knowledge of grammar in the abstract, and specifically English grammar. But if that is your only goal, again, it is just better to study English grammar directly.
What Latin alone will do is let you read the words of the ancients directly, and understand them in ways that reading in translation won't. The Roman republic was hugely influential on the founders of the United States, and it is difficult to fully understand the founders without understanding the Romans. Almost every English writer of significance before, say, 1900 was well versed in Latin, and enormously influenced by republican through medieval Latin literature.
Perhaps even more importantly, someone who studies classical civilizations realizes that there are things the ancients considers moral and unchangeable, like slavery, were neither. Other facets of society, such as love of family are unchangeable to this day. I hope that my kids can understand this and reflect upon modern life in the same way.