Dear Anthony,
I am assuming you can read the threads that Fr. Maximos referenced, but for the benefit of the members who cannot read Greek, here is a summary of the information in those threads, which is primarily based on works by Dr. Emmanuel Giannopoulos and Dr. Evangelia Spyrakou.
The reader/cantor belongs to the minor clerical orders. As such, he receives ordination from a bishop and is expected to lead an exemplary Christian life. This type of ordination is called χειροθεσία in Greek, whereas the term χειροτονία signifies ordination to one of the major orders (deacon/presbyter/bishop). In most sources the terms “reader” (ἀναγνώστης) and “cantor” (ψάλτης) are used interchangeably and appear to be equivalent in terms of hierarchical ranking. However, there are different services of ordination to each.
In the past readers/cantors wore bright vestments of various colors (e.g. purple, blue, red, orange, etc.), such as the phelonion (today worn only by priests and bishops), sticharion (today worn by clergy belonging to the major orders as well as altar servers), kamision (which was perhaps similar to the phelonion), sfiktourion (robe with wide sleeves and belt), etc. Evidence of this can be found in sources that date as far back as the 4th century (St. John Chrysostom). They also wore two different types of hats, the boat-shaped skiadion and the cylindrical, usually white, skaranikon, which was similar to a bishop’s mitre. The 24th Canon of the Synod of Laodicea (363-364) expressly forbids readers/cantors from wearing an orarion (worn only by deacons).
In the 17th century a more monastic appearance was adopted by all the clerical orders. Nowadays, during the performance of his liturgical ministry, a reader/cantor is allowed (or rather required by the Ecumenical Patriarchate) to wear an exorasson (pl. exorassa), which should not be exclusively associated with the office of a presbyter, or an anteri (pl. anteria). The vast majority of cantors wear exorassa. A sticharion (pl. sticharia) is also permissible. However, it is almost never used in Greek-speaking churches. I have only witnessed cantors/readers wearing sticharia once during a celebration of the Divine Liturgy of St. James the Brother of the Lord.