That display you want take a lot of pins to make it work. Look at the pins required in the lower part of this page. Arduino Playground - GLCDks0108
To do all of the things you are asking for, it is starting to look like you need something based on the 2560 mega.
There are cheaper boards out there but, here is one for example. Arduino Mega 2560 R3 (Atmega2560 - assembled) : ID 191 : $39.95 : Adafruit Industries, Unique & fun DIY electronics and kits