You can probably do it with a Duemilanove, but you need to do a little research on all the things (sensors etc) you want to use.
Logging data to SD can be done, displaying text on an LCD can be done, hooking up an accelerometer can be done.
You just need to know how each device is interfaced to Arduino to determine if the Duemilanove has enough I/O pins to do it all at the same time.
So you should take a piece of paper and write down exactly what it is you wnat to achieve. Then break it down and find out what sensors / input devices you need to achieve it, and then figure out what that requires from the Arduino board in terms of digital I/O, analog I/O, and storage etc.
There's really no magic way around this 
EDIT:
Another importanat point is: if you decide to use some of the many Arduino shields available for easy interfacing of sensors etc. then you should figure out which pins thet use and wheter they block for the usage of other pins, which some of them do.