The order of importance of being called up to the Torah (the 'Aliyoth) to the Torah are as follows:
According to the Peshat, the most important is Shelishee (the third portion). However, according to the Sod (the Qabbalah), the most important is Shishee (the sixth). After then the order is, Shelishee (the 3rd), Kohen (1), Lewi (2), Rebee'ee (4), Hamishi (5), and Mashlim (7). Mashlim, which is the seventh portion of the reading on Shabbath is actually the lowest one, even though it has a Qaddish. In fact, even though, it is very popular with mourners, the best Qomah ('Aliyah) for a mourner to go up for is Maphtir, especially if it one of the special readings that we have during the year.
(See Ben Ish hai, Parashath Toldoth, Shana Beh Othioth Yod Zahn & Kaf Aleph)
