Since you got a 14.4 I assume that vintage is not really the goal here. In that case I would recommend Lync by Jason R. Alward. The executable is only 37820 bytes so it is good for old computers. It is also much more well featured than the ubiquitous ProComm Version 2.3 (March '86) which at 143,457 is a bit on the large side. For sheer performance, I wouldn't consider anything else other than Lync, unless I wanted to be able to do everything under the sun, in which case Telix is the one.
Like most programs Lync has a host mode where you can chat, leave a message, or down/upload files. Give me a call and I'll let the modem answer and we can have a modem chat.
However since that machine came out in 1984 then perhaps you would like to consider the following which
all were released in 1983:
Hayes Microcomputer Products, Inc. Smartcom - II
IBM Personal Computer
PC-TALK III
Communications Program for The IBM Personal Computer by Andrew Fluegelman
"1-RingyDingy"(tm)
(C)Copyright 1983 by Jim Button Version 1.2
Kermit-86 version 1.2 (1983)
KERMIT is a family of programs that do reliable file transfer between computers over TTY lines. KERMIT can also be used to make the IBM PC behave as a terminal for a mainframe.