The Mixtrack Pro has an inbuilt sound card, so you’re going to be fine 🙂 And speakers aren’t essential when first learning, though I would look into buying some fairly soon, just so you can hear the tracks with a bit of punch 🙂
To the OPs question, I would think that it’s probably the cue/pgm issue that madman mentioned, it’s the knob above the browse knob, just make sure it’s turned to the left (cue) 🙂 If that doesn’t work you’ll want to have a look at your audio settings, to make sure you’ve got cueing set up properly.