There is no escape from memorizing the paradigms of the irregular verbs. I give my students a short list of the 100 most common/useful, and have them learn it by rote; I suggest that they post it in their bathrooms until they can rattle it off aloud to me: 'run-ran-run', 'come-came-come', etc. After that, the regular verbs are a snap.
Simple present is perhaps not the most useful tense to teach-- I would teach the present continuous first, if you are aiming for utility. With that, you can move to the 'be going to' future (also more common than the 'will' future) without adding a new form. And the present perfect should be taught soon also.
No doubt others have further advice for you. Enjoy!