Could someone please offer me some guidance on some kind of particular, SPECIFIC project that I could attemp, to "get my feet wet, so to speak"
I would suggest Kaggle learning projects - http://www.kaggle.com/competitions

Look for the ones in the 101 section that offer knowledge. There's many pre-made solutions ready, which you can ingest and try variations of.

Also, I have bookmarked a Comprehensive learning path – Data Science in Python, which among other things gives a few answers to your specific question.