上で【うえで】

上で after a た-form means "after doing, and on that basis": you do the first thing properly, then act on it. A noun of action such as そうだん相談 or かくにん確認 takes の上で in the same sense. It is formal, and it is what you meet in business Japanese and instructions.

The second half is a decision or a deliberate act that depends on the first. For two things that just happen in order, use てから: ×朝ごはんを食べた上で、学校に行った.

Dictionary form: "in doing"

After the dictionary form, 上で means "in doing", "for the purpose of": what matters, or what gets in the way, when you do that thing. The second half is usually a judgement such as たいせつ大切だ, ひつよう必要だ or かかせない欠かせない.

With a noun in this sense, 上で fits words like しごと仕事 and ほうりつ法律: "in terms of work", "in law".

上で or ために

ために gives the goal of an action: "do X in order to Y". 上で names an area and says what counts within it. Telling someone what to do for a goal takes ために: ×安全の上で、ヘルメットをかぶってください → 安全のために.