Aww, I remember going through the 1st birthday thing with my girls:)! It's tricky when the kids are so little, but it's such a big milestone! Keep in mind that your son won't remember it except for the pictures and videos you take, so keep it simple and think "memories" that you want to have and that you want to give him.
I agree that the BBQ is too chancy, especially in Chicago. The weather is too unreliable and you don't need any extra worries on that day! Is the party more for the kids or the adults? Do you have a rough idea of what you want to spend? I was an event planner for years, so I may be able to give you some ideas if you add some details. There are lot's of things you can do that are super fun and inexpensive!