Hoverduino? Data logging + LCD + Inputs?

I'm trying to figure out a way to hook up the arduino uno to a datalogging shield, have a 16x2 LCD, and use 5 analog inputs, and 5 digital inputs and one digital output.

Which parts are proving hard? The shield only fits one way, so it is not likely to be the problem area.

Which specific LCD? Serial LCDs only take one pin. Others take between 6 and 20 pins.

Which data logging shield? What pins does it use?

Is this possible?

With the right hardware, yes. With the wrong hardware, no. Mostly, it is the LCD that will be the limiting factor.