In Ancient Greek, it seems that there were various endings for agent nouns. Thomas Dwight Goodell's School Grammar of Attic Greek (1902) mentions -τηρ, -τωρ, -της, -εύς, -τειρα, -τρια, -τρις (-τριδ-), -τις (-τιδ-) (§405).
Goodell says that the first four are masculine, and the last four are feminine, but the table of examples in that section includes two -τωρ nouns that cross over between the masculine and feminine categories: ῥήτωρ "speaker" and ἵστωρ "one who knοws" (Goodell's definitions). I assume this means that these are what is called "common gender" nouns: grammatically feminine when they refer to a female person, and grammatically masculine when they refer to a male person. In contrast, συλλήπτωρ "helper" is shown as an exclusively masculine noun with a feminine counterpart συλλήπτρια.
Is this description accurate? If so, how frequent is each type of agent noun? Are there any ways to predict which ending(s) an agent noun will take, and whether an agent noun ending in -τωρ will be common gender or (exclusively?) masculine?