cyb3rfreak, if you just want to use lcd (as be80be suggested) you do not need rs232 at all as those old (3310, 5110, 6210..) displays are SPI and fairly easy to drive.
If you want to communicate between PIC and Nokia phone, then you do not need rs232 level shifter (that MAX chip) as both PIC and Nokia have same levels by default (0-5V) so no need to shift the levels to rs232 and then back to ttl.
With regards to communication between PIC and Nokia, you "cannot just send data and see it on the screen" as that would mean that your phone has some terminal emulation software, and most of them - do not, especially 3310
What you can do is talk to nokia 3310 using mbus protocol, google for it (few topics on this forum about it too) and make phone send sms, read sms from phone, manipulate data in phone etc... but this is "not easy". you cannot do that by just sending few codes to the serial port and the source code for this will not be few lines.
If you only want to use the
PCD8544 based display like in nokia 3210, 3310, 3315, 3330, 3350, 3410, 5110, 5120, 5130, 5160, 6110, 6150, 6210, note that PCD8544 works on 3V and your PIC works on 5V so you need to do some level shifting. These display's are great, they do not consume too much power and are very easy to use + they do not use too many pins... I use them non-stop with msp430f2xx uC's