You should focus on your opponent first, and learn how to react. Once you can properly defend and take advantage of openings, then focus on improving your own offense.
Even with a game like BlazBlue that has a Challenge mode with dozens of combos (many of them overcomplicated and unoptimized,) believe me when I say it doesn't mean a thing if your fundamentals aren't there (I aced Hazama's Challenges in CS but in actual gameplay my positioning and my usage of his chains was embarrassing.)
Honestly if you can properly perform all your character's moves without thinking about it, and understand the game's basic combo system (gatling vs. links, etc.) you're gonna be almost average. As long as you're not mashing and you're actually testing these moves out and figuring out their situational purposes, you're going to improve.
Combos eventually become necessary for above average to high level play, but I think at an average level, knowing how to perform basic gatling combos into a special or super is enough.
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