The advantage to it is, you've paid up front and so you will force yourself to go every week. Your child will go with you and help carry the vegetables home, which sparks some interest. You'll come up with recipes and try new things, which involves your child. He'll eat more than corn and watermelon because they're only in season part of the time. He'll also find out that locally grown produce that's really fresh and hasn't been sitting in nitrogen gas in a refrigerated space for weeks tastes a lot better than supermarket stuff.
The down side is, you have to eat what's in season, just like your grandparents did. In May, you aren't going to get corn. You're going to get spinach and kale and radishes and different types of lettuce. So you have to change your habits and not expect to eat your favorite vegetable every week forever. You can pick your own strawberries or buy fresh picked at the farm, but then when they're done, they're done. You have to be more excited for what's coming and not just mourn what season is past. You have to be as excited about beets as you are about berries, and that takes some adjustment because many of us are used to eating certain foods every week year-round. You have to be willing to try new things and find uses for the parts you'd normally never use (like cook the beets but use the greens too).
The cost is based on a certain amount every week. That doesn't mean that you can skip the first month and then load up on the stuff you love. You're going to get a pre-set amount so when your grocery bag is full, you're done for the week. So if that's not fun for you, you'll lose money on the deal, and you'll lose interest/momentum.
It kind of depends on how set you are, how adventurous you are, how committed you are to eating more variety. If you're a creative cook or willing to research recipes, and if you have a freezer to set aside your extras, it can work. Otherwise, just commit to going to the farm as a customer every week. If you find you are walking out empty-handed for 2 of the 5 months, you know you aren't ready. But you can also buy one batch of kale and try it out, or one bunch of beets or a new squash to try. Then you'll know for the following year. That's what one of our local CSA farms recommended to a friend of mine who has 2 grown daughters at home.