I write this article mostly just for myself: for making easier to check fonts, and to report in future. Because I noted some common patterns. Just in case: I'm not a font-maker, I'm still a user.

Cyrillic isn't just Russian

Well, it's very obvious statement. But from my expierence, it isn't so much. For the start, it would be nice to add at least all modern Slavic letters. You can add by a group as a stage.

Eastern group is Belarusian, Bulgarian, Russian and Ukrainian (with Rusyn). Southern one is the rest: Macedonian, Montenegrin and Serbian — basically, those alphabets which are based on an orthography by Vuk. As you may expect, a base is for both Eastern and Southern.

Vowels

Аa Ее Ии Уу Оо     # Base
   Ээ Іi Ыы    Ъъ  # Eastern
Яя Єє Її Юю Ёё     # └ Ioted
               Ьь  # Historical
   Лл Нн Рр        # Southern

Consonants

Бб Вв Гг Дд Жж Зз Кк Лл Мм Нн Пп Рр Сс Тт Фф Хх Цц Чч Шш  # Basе
      Ґґ                                              Щщ  # Eastern
      Ѓѓ Ђђ    З́з́ Ќќ Љљ    Њњ       С́с́ Ћћ       Ѕѕ Џџ     # Southern

Signs and semivowels [they're included in alphabets]

Ьь  Ъъ  Йй  Ўў  # Eastern
        Јј      # Southern

Some letters here, like some Montegerin ones, can be only with combining diacritics.

Still, don't forget to decompose letters for checking their visual. This may happen, mostly during some programming shenanigans. Also have a respect to zero-width non-joiner. It matters to Latin too: when I write something like i + &zwnj; + ◌́ U+0301, then, please, keep the dot, not replace it as under a normal condition.

About punctuations, it's basically the same as in Latin. I would only note, that some Ukrainians may use a modifie letter apostrophe instead U+02BC instead: an apostrohe U+0027, a signle [mostly right] quatation mark U+0027, and in some rare cases a grave accent U+0060.

Do you love history?

If so, then maybe you want add leters at least from Early Cyrillic, on which, I didn't mentioned before, Eastern group is based.

If you add a letter from one group, then it's better to add a whole group (if it's not from «not common»). And, yeah, if you add a group from «vowels», you add a corresponding group from «consonants» too. So, yeah, by this note adding ѧ but not ѩ is totally okay.

For some reason I was in a situation many times where a font has ѫ but not ѧ which is very strange at least for two reasons: it's a classic pair as ъ and ь, and by linguistics (at least for Eastern) ѧ is more important.

Vowels
Ѣѣ Ꙑꙑ Ѹѹ Ꙋꙋ # Base Ѵѵ Ѡѡ # Greek base Ꙇꙇ # └ not common Ѧѧ Ѫѫ # Nasals Ꙗꙗ Ѥѥ # Ioted Ѩѩ Ѭѭ # ├ nasals Ꙓꙓ # └ not common

Consonants
Ꙉꙉ # Base, not common (at least in Eastern) Ѯѯ Ѱѱ Ѳѳ # Greek base Ҁҁ # └ not common

Of course, there're more symbols, but those are usually enough.

Letters aren't alone

Surprise (not), but Cyrillic has diacritics too, as Greek or Latin. For some reason, it's very often omitted in fonts.

You could noted that before I divided symbols into groups: consonants, vowels and signs. Well, it will be helpful here, because we speak here about only vowels.

In Eastern those diacritics can be applied:

◌́ an accute U+0301

◌̀ a grave U+0300

In Southern (and Historical) you include the previous part from Eastern, and those:

◌̏ a double grave U+030F

◌̄ a macron U+0304

◌̑ an inverten breve U+0311

Try to keep one type diacritic the same for all letters. Because, as for an example, I saw many times where ◌̈ a diæresis U+0308 for ї and ё were different (by distance between dots, by hight from letter etc). And diacritics usually act as in Latin, for an example, [amost, just in case] any diacritic replace a dot within і. Also, її and ії are a common combination in Ukrainian, so itʼs better to avoid overlaping of dots here.

For reminding, some base vowels and consonants can be decomposed into a letter and:

◌̆ a breve U+0306

◌̈ a diæresis U+0308

◌́ an accute U+0301

I would note another obvious thing. All above is about standards. There're still other orthographies, including historical like by Hatcuk or Maksimovitch, Cyrillic-based transcriptions and so on may have other diacritics. So if your diacritic symbols will cover more letters, or be more independ from letters, then it would be better.

<details><summary>All letters</summary>

Composed — Decomposed — Without diacritic: CODEBLOCK5

Groups:

Top: letters should be displayed correctly

Middle: as a bonus example

Bottom: historical letters

Regular
Аa Ее Ии Уу Оо Лл Нн Рр Ээ Іi Ыы Ъъ Яя Єє Її Юю Ёё ----------------- Ьь Ѣѣ Ꙑꙑ Ѹѹ Ꙋꙋ Ѧѧ Ѫѫ Ѩѩ Ѭѭ Ꙗꙗ Ѥѥ Ꙓꙓ Ѵѵ Ꙇꙇ Ѡѡ

◌́
А́á Е́е́ И́и́ У́у́ О́о́ Л́л́ Н́н́ Р́р́ Э́э́ І́í Ы́ы́ Ъ́ъ́ Я́я́ Є́є́ Ї́ї́ Ю́ю́ Ё́ё́ ----------------- Ь́ь́ Ѣ́ѣ́ Ꙑ́ꙑ́ Ѹ́ѹ́ Ꙋ́ꙋ́ Ѧ́ѧ́ Ѫ́ѫ́ Ѩ́ѩ́ Ѭ́ѭ́ Ꙗ́ꙗ́ Ѥ́ѥ́ Ꙓ́ꙓ́ Ѵ́ѵ́ Ꙇ́ꙇ́ Ѡ́ѡ́

◌̀
А̀à Ѐѐ Ѝѝ У̀у̀ О̀о̀ Л̀л̀ Н̀н̀ Р̀р̀ Э̀э̀ І̀ì Ы̀ы̀ Ъ̀ъ̀ Я̀я̀ Є̀є̀ Ї̀ї̀ Ю̀ю̀ Ё̀ё̀ ----------------- Ь̀ь̀ Ѣ̀ѣ̀ Ꙑ̀ꙑ̀ Ѹ̀ѹ̀ Ꙋ̀ꙋ̀ Ѧ̀ѧ̀ Ѫ̀ѫ̀ Ѩ̀ѩ̀ Ѭ̀ѭ̀ Ꙗ̀ꙗ̀ Ѥ̀ѥ̀ Ꙓ̀ꙓ̀ Ѵ̀ѵ̀ Ꙇ̀ꙇ̀ Ѡ̀ѡ̀

◌̏
А̏ȁ Е̏е̏ И̏и̏ У̏у̏ О̏о̏ Л̏л̏ Н̏н̏ Р̏р̏ ----------------- Э̏э̏ І̏ȉ Ы̏ы̏ Ъ̏ъ̏ Я̏я̏ Є̏є̏ Ї̏ї̏ Ю̏ю̏ Ё̏ё̏ ----------------- Ь̏ь̏ Ѣ̏ѣ̏ Ꙑ̏ꙑ̏ Ѹ̏ѹ̏ Ꙋ̏ꙋ̏ Ѧ̏ѧ̏ Ѫ̏ѫ̏ Ѩ̏ѩ̏ Ѭѭ Ꙗ̏ꙗ̏ Ѥ̏ѥ̏ Ꙓ̏ꙓ̏ Ѷѷ Ꙇ̏ꙇ̏ Ѡ̏ѡ̏

◌̄
А̄ā Е̄е̄ Ӣӣ Ӯӯ О̄о̄ Л̄л̄ Н̄н̄ Р̄р̄ ----------------- Э̄э̄ І̄ī Ы̄ы̄ Ъ̄ъ̄ Я̄я̄ Є̄є̄ Ї̄ї̄ Ю̄ю̄ Ё̄ё̄ ----------------- Ь̄ь̄ Ѣ̄ѣ̄ Ꙑ̄ꙑ̄ Ѹ̄ѹ̄ Ꙋ̄ꙋ̄ Ѧ̄ѧ̄ Ѫ̄ѫ̄ Ѩ̄ѩ̄ Ѭѭ Ꙗ̄ꙗ̄ Ѥ̄ѥ̄ Ꙓ̄ꙓ̄ Ѵ̄ѵ̄ Ꙇ̄ꙇ̄ Ѡ̄ѡ̄

◌̑
А̑ȃ Е̑е̑ И̑и̑ У̑у̑ О̑о̑ Л̑л̑ Н̑н̑ Р̑р̑ ----------------- Э̑э̑ І̑ȋ Ы̑ы̑ Ъ̑ъ̑ Я̑я̑ Є̑є̑ Ї̑ї̑ Ю̑ю̑ Ё̑ё̑ ----------------- Ь̑ь̑ Ѣ̑ѣ̑ Ꙑ̑ꙑ̑ Ѹ̑ѹ̑ Ꙋ̑ꙋ̑ Ѧ̑ѧ̑ Ѫ̑ѫ̑ Ѩ̑ѩ̑ Ѭѭ Ꙗ̑ꙗ̑ Ѥ̑ѥ̑ Ꙓ̑ꙓ̑ Ѵ̑ѵ̑ Ꙇ̑ꙇ̑ Ѡ̑ѡ̑

</details>

Localization

There're at least three traditions of Cyrillic:

Bulgarian, also can be called as a straight cursive

Southern

Eastern, but without Bulgarian

Some notes:

Cursive Ukrainian ґ doesn't act as г, thus it's better to keep this letter as in Ukrainian even for non-Eastern styles too.

Any diacritic symbol over ligature letters (ioted + uk) can be placed just at the middle, and it's a usual practice. But for more stylish way, you can put it over the second letter; as an example: in a case of ю́, put ◌́ just over o. Otherwise, as it was said, put it just at the middle, but higher a whole letter, which's important in case of Bulgarian style. Sadly, but, yeah, it may bring common problems for any tall letters in some cases.