Displaying base THAC0 is important because it changes as you level, and for different classes it changes at different rates.

As for your modified (actual) THAC0, you're getting worse results with a wooden staff because you don't have the staff proficiency, and are getting the penalty for it. So you're getting +3 to hit from your strength, and -2 from the non-proficiency penalty, for 19 total. For the two-handed sword, you're getting the +1 proficiency bonus instead of -2, along with some other bonuses to things like damage and speed, for a total THAC0 of 16. Unarmed attacks don't have a proficiency, so get neither bonuses nor penalties from it, so you're just using your strength modifier for a total of 17.