The answer to that is simple - there is no single answer! How long do the w-melons and cantalopes take to mature? That should be on the seed packet. If your growing season is long enough to accomodate them, you might as well sow them directly. I would cushion your growing season by 10-15 days to allow for any crappy weather early on that might cause the plants to hunker down for a while.

If you need them ripe sooner (for competitions or family reunions, etc.) then start them indoors. I would not do this sooner than 2 (least) to 5(most) weeks before last frost-free date. Two weeks isn't a lot of head start so you don't gain much and after 5 weeks you may have something like Invasion of the Bodysnatchers growing in your house!

I did giant corn and sunflowers last year and planted them direct, which worked fine. They were both about 90 days. I am planning on starting the sunflowers indoors this year, but only because I love gardening and that will help with my early season itch. I have already been out poking around my perrenial beds and it snowed again today!!!!!!!!!!!!