The ones that you've listed generally should be enough for serial communications with hardware flow control. Newer UARTs, e.g. TL16C550C (the 'C" suffix is important) can even be programmed to do automatic RTS/CTS.
Serial mice do "steal' power from serial port (as RS-232 does not include any power signals vs. XT, AT, or PS/2 keyboard/mouse ports). So they might use either RTS or DTR lines to get the power or both... I think usually there is a diode or a two are connected to these signals, plus a Zener diode or a voltage regulator to reduce the voltage to 5V or so.
For example, see the datasheet for the
EM83701 mouse controller, it has the schematic.
If I recall correctly, the PC side of the RS-232 should have 3 drivers and 5 receivers. You can use two MAX232's but then you'd not have one of the receivers (and one extra driver). If you're not planning to use a modem, you can get away without implementing the RI (Ring Indicator) signal, and save a receiver that way. At least that what I did while back when building an ISA serial port board (see attached schematic).
Alternatively, if you have +/-12V available, you can use a
GD75232 driver/receiver or similar. It has 3 drivers and 5 receivers as required for an IBM PC compatible RS-232 port.
-Sergey