Firstly ask yourself the question what do I enjoy the most? For some that's MTTs (like me) for others that might be cash. I'd just stick with that.
Having said that though, for any tournament player it wouldn't hurt to have a solid cash game background as most tourney players suck playing deepstacked compared to most cash game players (so do I tbh, 100bb deep is not my comfort zone).
If you have any kind of aspirations in poker, I think, you need to learn both tournament and cash game play to keep the most amount of options open to yourself. And as you say to not suck completely in the early blind levels of tournaments.
Its not great to jump back and forth every session at least not in the beginning. But maybe take 3 month, where you grind cash games and then take 3 month, where you grind STTs or small MTTs like 18-45 man SnGs.
If you then find, that you enjoy the tournament format more, then its time to get into larger MTTs, as often as you have time for it. If you enjoy cash more, then go back to cash and try to grind it up there.