If you commit today (or before ivy day at least) you have a decent chance at BJ I believe, but Snitchcock is probably full. If you want a single, BJ is better as Snitchcock doesn’t have many singles for 1st years, and BJ is mostly singles.
My S1 is a 4th year in BJ, loves his single but leaves his door open when he wants to socialize and goes to the house lounge to meet up with others as well. . Since most rooms are singles, the house system works really well to socialize everyone with activities and meetings.Works great for him.
You have priority with all your choices over anyone committing after you,so whoever commits now has a better chance to get into on of their choices. And yes, you could cancel your commitment but will lose the $500.
Congrats on your acceptance, and welcome to UChicago!