First off, welcome and hope you enjoy your journey into the ardu-verse!
(as best as i can answer)
a) of course! I would recommend using a serial lcd coupled with a blueSmirf bluetooth module from Sparkfun [costly option approx $200]
b) Yes. Once again, Sparkfun carries a specific xbee shield tailored for the lilypad arduino and you could couple this with another xbee module attached directly to your lcd of choice. [bit more affordable <$100]
I've been looking to accomplish a similar project and would be glad to help (despite my lack of pro skills) once you make your decision on wireless options.
Would it be possible for you to expand on your points guys, I am over the super slow variety of learners! Which specific arduino and xbees would I need to accomplish this?! And which xbee would I need to attach to the LCD display?
Basically would it work to communicate from my mac through an arduino Duemilanove with an xbee shield to another xbee module (which one?!) that is attached to a serial LCD?
yes their is a more cheap and good way of doing this.
just buy a tlp434a(radio frequency 434Mhz transmitter),rlp434(reciever), connect it to the arduino and begin sending data and recieving via serial.
off course the arduino will be also connected to an lcd using the 4bit library interface .
The Arduino -> xbee <-> xbee -> serial LCD is a litle more complicated than that. Remember that the xbee is a 3.3V device.
So you'll either have to use level shifters between the Arduino/xbee and the xbee/serial LCD, or run the arduino at 3.3V and be sure to get a 3.3V serial LCD (or some combination of the above).
It's still doable, it's just a little more complicated.
If it's just a one-way link, then the simple 315/433MHz transmitter/receiver pairs are an option depending on the needed range. But this is then complicated by the need to have a more robust communications protocol at either end as you can't just pipe serial data through these links. You would need to use something like VirtualWire (look in the playground) and put an Arduino (or at least a programmed ATMega168) at each end to handle the communications. If you did that you could eliminate the expensive serial LCD and just use an inexpensive base LCD module connected to the receiver Arduino.
I'm doing something very similar to this with a remotely located RFID panel. I then send the serial RFID tag data wirelessly to my home automation system.