When is a comma appropriate when using "that is"

I agree with Janus BJ's comments above. You can also use the Latin abbreviation i.e.:

In the first instance, efficiency needs to be evaluated; the most efficient choice, i.e. the choice that minimises unnecessary requirements, is the preferred outcome.

Note that some style guides specify a comma after the "i.e.", on the grounds that this is in accord with the actual meaning of the Latin id est (which means "that is"). The ostensible logic for this is that because one would follow the English that is with a comma, it is also necessary to use one with i.e.

This seems incredibly pedantic to me (because it resolves no ambiguity), as well as intruding an unnecessary pause in the flow of the sentence. So I make no apologies for not using one. :-)

The commas aren't a problem per se: it's just that the sentence has a lot of short sections, and it's not immediately clear how they relate to each other. You say you often overuse commas, and I suspect it's a result of trying to cram too much into each sentence: I used to have a similar problem, so I recognise the symptoms.

In general, I'd advise writing shorter sentences. Where you would normally use a semicolon or colon, break the sentence there instead. Then, when you come to a situation like this one, replace commas with punctuation that shows the relationship of the different parts of the sentence.

To take this particular example:-

In the first instance, efficiency needs to be evaluated. The most efficient choice (that is, the choice that minimises unnecessary requirements) is the preferred outcome.

(As mentioned in the comments, you can use parenthetical dashes instead, and that's really a question of personal preference.)

You might even like to think about the rule of having one thought per sentence. Short sentences like the following aren't always appropriate to the tone or expected style, but they can help marshal your thoughts.

In the first instance, efficiency needs to be evaluated. The most efficient choice is the preferred outcome. That is the choice that minimises unnecessary requirements.

Looking at this one-thought-per-sentence version shows us another way to write the idea: a way that doesn't look like a children's book.

In the first instance, efficiency needs to be evaluated. The preferred outcome is the most efficient choice: that is, the choice that minimises unnecessary requirements.

Here, I've swapped the order of your main point, which might not fit the context so well, but you can see how it works in other cases.