Leaving aside the traditional Tikkun Leil Shavuot which includes Chumash, Nach, Mishnah, Gemara, Halacha, Kabbalah etc. the increasingly common current practice is to study a wide variety of materials.
Is anything discouraged and is anything particularly encouraged?
To add some information to the practice of saying Tikkun Leil Shavuot-
There is a machloket regarding saying Mishnayot, The Chid"a and others are of the opinion to omit them but the Shla"h and others are of the opinion to say them.
See footnote 16 (ט”ז) on page 53 (נ”ג) (page 9 of the PDF) here by Rabbi Shmuel Yismach.
The traditional Tikkun Leil Shavuot contains excerpts of each parasha, every book of the remainder of Tanach, Mishnah, Kabbalah and a list of the 613 mitzvot. The common current practice is well summarised in the bolded passage below from https://www.chabad.org/library/article_cdo/aid/5529328/jewish/Why-Tikkun-Over-Deep-Learning.htm
There is a widespread custom to stay up the entire night of Shavuot learning Torah. While some spend the night learning whatever Torah topic they fancy, many have the custom of specifically learning a special booklet known as the Tikkun Leil Shavuot (“The Fixing of the Night of Shavuot”).
In large communities such as my home town of London there is a dizzying array of Tikkun Leil Shavuot study programmes on offer at almost every Shul. The programmes held at some shuls have shiurim which address Shavuot related topics, others take the opportunity for a thematically linked deep dive leil limmud, others host imaginative multi-streamed offerings with something for everyone. The key is to share the joy of the communal study of Torah.
In my experience the only subjects that are generally avoided (or discouraged) are those relating to mourning and similar topics which are regarded as "Tisha b'Av material" rather than as appropriate for Tikkun Leil Shavuot.
In his answer @Yoreinu references a machloket regarding including Mishnayot in Tikkun Leil Shavuot. In that regard it is fascinating to read this article Salonika, 1533: The Most Famous Tikkun Leil Shavuot at https://jewishjournal.com/commentary/columnist/349083/salonika-1533-the-most-famous-tikkun-leil-shavuot/
and in particular this passage:
Rav Alkabetz describes Rav Karo studying Mishnah on the night of Shavuot in Salonika in 1533, and he says this night was like a reenactment of the Revelation at Mount Sinai, but instead of Moses the Prophet, this time the revelation came to the great mystic Rav Yosef Karo. On that night, when Rav Karo studied Mishnah, Rav Alkabetz and all of the Haverim heard the voice of the Shekhina emerge from Rav Karo’s mouth, saying: “Cease not from studying Torah, for a thread of mercy is stretched out over you, and your Torah study is pleasant to the Holy One blessed be He. Stand upon your feet and raise me up.”
