It is possible to only learn the printed Cyrillic Alphabet and get by without any cursive. Cursive is only used for italics, handwriting or calligraphy and if you are only typing on a computer then learning it early can be unnecessary.
Short List of Italics
Italic letters look mostly the same with a few exceptions
Гг – Гг
Дд – Дд
Тт – Тт
Complete List of Italics
Vowels Hard Аа – Ээ – Ыы – Уу – Оо Аа – Ээ – Ыы – Уу – Оо
Vowels Soft Яя – Ее – Ии – Юю – Ёё Яя – Ее – Ии – Юю – Ёё
Silent Hard sign Ъъ Ъъ
Silent Soft sign Ьь Ьь
Semi-vowel Йй Йй
Constonants Voiced Бб – Вв – Гг – Дд – Жж – Зз Бб – Вв – Гг – Дд – Жж – Зз
Constonants Voiceless Пп – Фф – Кк – Тт – Шш – Сс Пп – Фф – Кк – Тт – Шш – Сс
Constonants Always Voiced Лл – Мм – Нн – Рр Лл – Мм – Нн – Рр
Always Voiceless Хх – Чч – Щщ – Цц Хх – Чч – Щщ – Цц
Hissing Always hard Жж – Шш – Цц Жж – Шш – Цц
Hissing Always soft Чч – Щщ Чч – Щщ
It is best to learn cursive by writing it, then trying to read your own notes a few days later.
Below is a practice sheet with the stroke order for each letter. [1]
Then practice how to join the letters with some words. Notice the hook before л and м [2]
If you aren’t careful how you join the letters, then your notes will trend towards an incomprehensible series of uuuuuuuuu looped together.