My answer is almost the same as Dave's in principle. I hope it brings something new to the table by introducing the notion of "transcribing" Kanji words into Japanese:

When I studied 漢文 (かんぶん) in my high school days, I learned that transcribing Kanji words into full Japanese phrases can help understand them better. Kanbun is "a Japanese method of reading annotated Classical Chinese in translation" (Wikipedia).

If we combine 表示 with each of the four characters 不・非・無・未, and skip the details, they get transcribed as:

不表示 → 表示せ不 (ず)

• isn't, doesn't - mostly negates verbs and adjectives
• may add unfavorable connotation
• 「ページ不表示について」 When pages don't get displayed. - source

非表示 → 表示に非ず (あらず)

• doesn't equal ..., doesn't belong to ... - mostly negates nouns
• 「広告を非表示にするプラグイン。」 Add-on that turns off ads.

無表示 → 表示無し (なし)

• doesn't exist - negates existence = absence
• may add unfavorable connotation
• 「カロリー無表示のおにぎりを売っている。」 They sell onigiris with no calorie display. (emphasis is on the absence of display)

未表示 → 未だ (いまだ) 表示せず

• doesn't/isn't ... yet - negates completeness
• 「未表示のリンクの色は青にしてください。」 Please set the color of unvisited links to blue.

In theory, if you reverse this process - by finding the right phrase using either of the four Kanjis that matches your intention - you should be able to get the correct Kanji compound word.

Note: Definitions are taken from wikibooks on Kanbun and a study material by a Kanbun enthusiast.

Note 2: In case of 表示, "不表示" and "非表示" don't have much difference in meaning, although 非表示 is the prevalent one. My guess is that 非表示 is more neutral, and therefore more versatile and widely used.

My answer is almost the same as Dave's in principle. I hope it brings something new to the table by introducing the notion of "transcribing" Kanji words into Japanese:

When I studied 漢文【かんぶん】 in my high school days, I learned that transcribing kanji words into full Japanese phrases can help understand them better. Kanbun is "a Japanese method of reading annotated Classical Chinese in translation" (Wikipedia).

If we combine 表示 with each of the four characters 不・非・無・未, and skip the details, they get transcribed as:

不表示 → 表示せ不 (ず)

• isn't, doesn't - mostly negates verbs and adjectives
• may add unfavorable connotation
• 「ページ不表示について」 When pages don't get displayed. - source

非表示 → 表示に非ず (あらず)

• doesn't equal ..., doesn't belong to ... - mostly negates nouns
• 「広告を非表示にするプラグイン。」 Add-on that turns off ads.

無表示 → 表示無し (なし)

• doesn't exist - negates existence = absence
• may add unfavorable connotation
• 「カロリー無表示のおにぎりを売っている。」 They sell onigiris with no calorie display. (emphasis is on the absence of display)

未表示 → 未だ (いまだ) 表示せず

• doesn't/isn't ... yet - negates completeness
• 「未表示のリンクの色は青にしてください。」 Please set the color of unvisited links to blue.

In theory, if you reverse this process - by finding the right phrase using either of the four Kanjis that matches your intention - you should be able to get the correct Kanji compound word.

Note: Definitions are taken from wikibooks on Kanbun and a study material by a Kanbun enthusiast.

Note 2: In case of 表示, "不表示" and "非表示" don't have much difference in meaning, although 非表示 is the prevalent one. My guess is that 非表示 is more neutral, and therefore more versatile and widely used.