Whether the outcome is something you control
Each one below is our full write-up of that form, in the order worth reading them. Nothing is summarised — you are looking at the same pages the grammar index links to, put next to each other.
in order to; for the sake of; because of
V-plain / N + の + ために
Purpose when the verb is something you control: 日本語を勉強するために日本へ来ました.
For things you can't control, use 〜ように instead (聞こえるように大きい声で). ために can also mean cause: 事故のために電車が遅れました.
so that ~ (something one can't directly control)
V-potential / V-ない + ように
The counterpart to ために. Use it when the result isn't a deliberate act: 忘れないようにメモします, 見えるように前に座ります.
The giveaway is the verb before it — potential, negative, or an intransitive change of state.