Errrrr, I’m no expert, and I’m confused by your question, slightly, but I think my answer will clarify the situation for you.
Your question applies only to C-Groove.
Level-3 supers don’t do literally 3-times the damage as level-1s…maybe close to 2x the damage. Level-3s in this game DO have higher priority than level-2s, and ESPECIALLY level-1s. You can easily get knocked out of most level-1s, so it’s usually best to use those in a combo only. So the higher the level of super you use, it’s not just a damage increase but a priority increase.
I just re-read what you typed, and “or so” part might be the only part of your question that confused me 
Level-1 means 1 bar of super energy; level-2 means you have 2 bars of energy, etc…
There is only ONE punch or kick button that you can press to get a level-3 super to come out: level-3s must always be done with the fierce or roundhouse button (depending on whether it’s a kick super like Chun Li’s kick super, or a punch super like Balrog’s Super Dashing punch, etc.).
You can do a level-2 super with the strong or forward buttons, but if you have only 2 bars of super energy available, you can press fierce or roundhouse and you automatically will do a level-2 super, because you do not have ENOUGH super bars to do a level-3, so the game does the next best thing and gives you a level-2.
You can do a level-1 super with the jab or short buttons whenever you have 1, 2, or 3 bars of super meter available. If you have only 1 bar of energy, you can press ANY punch or kick button and get a level-1 super to come out, but it’s better to press jab or short if you ONLY want to use 1 bar of super meter.
There is only ONE time I can think of, when you would want to press a punch or kick button that is not intended for a specific level of super.
It’s hard to explain without going right into the example, so I’ll just do that.
Let’s say you have ALMOST 2 bars of super meter, and you just hit the opponent, leaving them open for a combo, and you want to use a super in that combo for more damage. You know your opponent won’t die if you hit him with a combo that ends with a level-1 super, and you want to do a level-2 super in your combo, if possible. It’s hard to pay attention to your super bar at the same time that you do your combo, so you can’t tell at that VERY MOMENT if you hit your opponent enough to fill up your bar to 2 levels, for a level-2. If you press jab or short, you will definitely only do a level-1 super, but you might suddenly have 2 bars, right before you combo/buffer into super, so you press strong or forward instead. If you have 2 levels stored up, you’ll do a level-2; if you still have only 1 bar full, you’ll do a level-1, but at least you know that you didn’t do a level-1 instead of a level-2, which of course would do more damage.
That is a rare case during a match, because usually you’ll get the chance to check your super meter before setting up a combo that contains a super in it, but it’s helpful for that occasional victory you otherwise would have missed the chance to get!