Saroma writes: Do you pitch your spec scripts to the producers/creators of the shows?
No. Writers write spec scripts (sample episodes of existing TV shows) as examples of their work, usually so they can get a job on the writing staff of a show. (And generally, a different show; I've heard it's poor form, for example, to use a TWO AND A HALF MEN spec to try to get a staff job on TWO AND A HALF MEN.) Specs are useful because they demonstrate that a writer can mimic the characters and tone of another person's show, and therefore be a good addition to a staff. You don't really pitch the idea to anyone except your friends and, if you have them, your agent or manager. People like producers and creators wouldn't hear about a spec until it's done and someone sends it to them as a writing sample.
In recent years there has been a trend toward using original material (pilots, plays, features, short stories, etc.) as writing samples instead of specs. The idea is that original material gives readers a better sense of who you are as a writer - what your individual voice is, what unique characteristics you'd bring to a staff, etc. But since specs are still used (and only specs are considered in many fellowships and workshops, like the ABC/Disney Fellowship and the WB Writer's Workshop), it's probably a good idea to write both specs and original material.
Personally, I recommend tackling a spec first. The characters and world have already been created, and you'll have several episodes to watch, break down and use as templates. You also might check out the old posts from Jane Espenson's blog - she wrote a lot about perfecting your specs and pilots.