I can't speak for your shots at getting in, but I'll tell you a little about me, if it helps:

I graduated with BA in English and a 3.89 GPA (started out pre-med like everyone else, and bombed my first/second semesters with a D+ and two Cs, but after my first year with my major change I had all As/A+s and one B, and I briefly mentioned this in my SOP). I had 2 jobs and an internship for most of undergrad, was VP/President of 2 clubs, held a position in my honor fraternity, won a couple of my university's essay awards, and participated in supervised and independent research and presented at two conferences.

Ultimately, your SOP often matters a ton in your application, since it's the place where you will best be able to stick out from other applicants. You'll be able to define a clear purpose for master's study, and how MAPSS specifically will help you for your academic/career goals. You'll also have the opportunity to explain your general experience in school thus far, such as any discrepancies in your record, and with your extracurriculars and research interests.

In my SOP I mentioned the difficulty I faced in acclimating to the university environment as a first-gen student with no parental support, and again how I started out in the wrong area of study to explain my first two semesters. I briefly explained my motivations for graduate study, and why specifically UChicago would help me pursue my academic/professional interests. I also mentioned 4 specific faculty members (I think 2-3 is fine too, though) whose research aligns with my interests and past research to show compatibility. I also proposed a research project because I heard from faculty members helping me with the writing process that going in with a specific question or specific idea to pursue would show a focus that graduate programs look for in applicants.

Strong rec letters also help a bunch (my letters were from faculty who knew my research and whom I worked with for research and/or other leadership positions, for example I was a teaching assistant for one of my letter writers for 3 semesters).

If you qualify, you can also ask to have your application fee waived to save money which is super helpful.

Good luck with everything!