I'm thinking about using the Arduino Ethernet, it has everything I need and is a bit cheaper than a 2009/Uno + Ethernet Shield.
Yes, it is, but keep in mind, that you also need some kind of USB2Serial adapter because the Arduino Ethernet does not have that on board, the UNO has.
Is there any LCD shield that is compatible with the Arduino Ethernet?
This one http://www.nuelectronics.com/estore/index.php?main_page=project_lcd seems to be, at least the schematics does not show a usage of the SPI interface of the Ethernet shield. You might have problems though to access the SD card (pin 4).
do you think the flash space on the ATmega328 will be enough for my project?
If you include only the necessary features and put the rest on the SD card, I guess you'll have enough flash for your project.