For the bulb, I recommend you get a mains to DC transformer and use a low voltage bulb. Then control it by a transistor (or transistor + relay) on the low voltage side. You really don't want to combine mains voltages with home made circuits and moisture. For example, transforming the mains voltage to 12V DC would enable you to use any automotive bulb, giving you a wide choice of wattages.
I don't know how to drive a Nokia lcd 5110 display but there are plenty of small LCD displays that are easy to drive, and if you can't find how the Nokia screen works then using a known display might be the easier solution.