Summary of Key Characters
Enclosed Alphanumerics U + 2460 - U + 2473
"U + 2474 - U + 24E9 *
"U + 24EA - U + 24FF
Miscellaneous Symbols U + 2600 - U + 2607
"U + 2618 - U + 2618
"U + 260E - U + 260F
"U + 2614 - U + 2615
"U + 263D - U + 2653
"U + 2660 - U + 266F
Symbols and punctuation U + 3000 - U + 303F
Hiragana U + 3040 - U + 309F
Katakana U + 30A0 - U + 30FF
Katakana phonetic U + 31F0 - U + 31FF
Enclosed letters and months U + 321F - U + 325F *
"U + 3280 - U + 32FF *
Unified Ideographs ext. A U + 3400 - U + 4DB5
Unified Ideographs U + 4E00 - U + 9FBB
Compatability ideographs U + F900 - U + FAFF
Compatibility forms U + FE30 - U + FE4F
Full-Width Roman U + FF00 - U + FF5E
Half-Width Katakana U + FF61 - U + FF9F
Full- and Half-Width Symbols U + FFE0 - U + FFEE
Unified Ideographs ext. B U + 20,000 - U + 2A6D6
Compatability ideographs supplement U + 2F800 - U + 2FA1F
* = Lower priority
Full explanation
Do not forget about the full-sized novel, which is often used for the Japanese alphabet (FF00-FF5E) and half the width of the katakanana (FF61-FF9F). You will probably also need full and half-width characters (FFE0-FFEE).
It can be argued that the Kanbun annotation (3190-319F) is usually not used. Kanbun and the old Japanese style, which uses all Chinese characters (without Hiragana or Katakana) with a different set of grammar rules, usually taught at school. These annotation labels will not be used unless someone tries to explain how to read / understand one of these passages, which is probably unlikely. It may be included for completeness, but is probably not a high priority.
CJK compatibility (3300-33FF) is usually used by newspapers in the print media, but it will almost certainly not be used by the average audience (I have not seen it on the website). In any case, they have equivalent long forms (for example, ㌘ can be written as グ ラ ム), so this also belongs to the non-essential category.
The CJK Radicals (2E80-2EFF) application is also immaterial, but can be used. They are not complete characters, but the "radical" (basic part) of the characters. They can be used to explain the character’s conclusion, but are unlikely to be used in normal language use.
CJK Strokes (31C0-31E3) is the same as CJK Radicals and is likely to be even less likely to be used in everyday use.
The first part of the Enclosed CKJ Letters and Months (3200-321E) is not needed. These are Korean characters. Same thing with (3260-327F). The rest of the page has a low level of use, but I would include it for completeness, because someone would probably try to use it at times. But you can consider them lower priorities.
The rest that you called up on your initial list are important.
Also not listed Enclosed Alphanumerics (2460-24FF). Cyclic numbers (2460-2473 and 24EA-24FF) are used relatively frequently. However, the workaround, the number in brackets, and the period of numbers (2474-24E9) may be omitted as non-essential.
In addition, it would be useful for you to include various characters (2600-263C), although some of them are used more often than others. Absolutely important ones include some conditional weather symbols (2600-2607), trefoil (2618), telephones (260E-260F), an umbrella and a hot drink (2614-2615), astrology and zodiac symbols (263D-2653), and a card game, hot springs and musical symbols (2660-266F).