I find that the mazurkas are an acquired taste, personally. Some of the waltzes and nocturnes can provide a good jumping off point:
Waltzes:
op. 64/no. 2 (C-sharp minor) or no. 3 (A-flat major)
op. 69/no. 1 (A-flat major)
Nocturnes:
op. 55/no. 1 (F minor)
op. posth. 72/no. 1 (E minor)
There are also some fairly quick learns in the op. 28 preludes (E minor, A major, B minor, C minor, D-flat major; my favorite, although a bit harder due to speed, is the G major) that will give you a sense of his style.