Learn about whatever possible. There's no set limit for knowledge or assessment, even at the EMT level. Especially if you start in IFT, look at your patient's charts and their listed medications. Begin to correlate them with their medical history and research what they're used for and how they work. Ideally, you want to get to the point where you can look at a med list and have some pretty good guesses about their medical history. Many EMTs don't know many of these meds or don't care enough to learn, but I do think they can make you a stronger clinician.
Learn generic and trade names, learn drug classes, and learn common endings of meds (ie -lol=often beta blockers, -pril=many ACE inhibitors).
I'd say you should be at least be familiar with a variety of beta blockers, ARBs, ACE inhibitors, oral anti hyperglycemics, antibiotics, steroids, anti epileptics, inhaled beta agonists and other COPD/asthma meds, pain meds (opiate and NSAID), benzos, diuretics, SSRIs, MAOIs, and try to recognize the rare but relevant TCAs. Learn to recognize blood thinners, particularly the less common ones besides just warfarin.
This sounds like a lot, but the more you see all of them (and these really are all quite common), the more they'll begin to make sense. Good luck!