Why didn't Gollum ever go to the Shire to search for Bilbo? He knows about the Shire as when hes being tortured he says "Baggins...Shire". In the movie that is. Your right about Mordor however, I've reread the first few chapters since I asked the question. He makes his way to Mordor. After this he is imprisoned by the elves. He then escapes from the elves.
Why was Frodo so resistant to the ring? Gandalf referred to him as being one of the "River folk" and not "that unlike a hobbit" I believe. (Quotes probably aren't exact).