One user accesses the line at any one moment. The connection is as fast as the slowest between your modem and the modem at the other end. You need about 56K of bandwidth for a database server which is frequently accessed by multiple persons. A handful of students can access the Internet with this type of access. A T1 line is good for extensive data transfer and video conferencing by many users at once.
Situations vary a lot from one phone company to the next.
The problem with ordinary voice lines are that each call is a different circuit, hence unreliable. A leased analog line could be a solution. It eliminates random circuit selection problems, and with various types of line conditioning, there are satisfactory speeds available. Charges are monthly regardless of the amount of usage. If the other school is a long distance call, you may be able to take advantage of remote call forwarding.