First project - climate controlled iguana cage

As my first arduino project I am building a climate-controlled cage for my pet dinosaur. I am totally new to this and would like it if someone could make sure sure that my plans will work before I try to buy anything!

I have soldered my Bare Bones Board together and gotten the Blink sketch to work.

I need to control temperature (90F - 95F daytime, >78F nighttime) and humidity (65%-75%). I also need to turn the light on/off every 12 hours.

My plan is to place the BBB near the basking spot, in such a way that it is covered and the iguana is unable to obscure line-of-sight with the heating element (and so that he is unable to mess with it at all).

I plan to power my BBB with a wall power adapter ($10) and use a SHT15 ($29) to test the temperature and humidity.

To display the current temperature, humidity, and time I will include a 2x16 LCD display ($11). To change the time and month (to simulate seasonal changes) I will use three push buttons.

To turn my light and heat on and off I will use two relays (2x $9) (note: I am on US power, that is an Italian company, and have zero experience).

To increase the humidity.. I'm not certain what I will do. I have a spray bottle (similar design as this) and thought about using a motor to drive the plunger down but am afraid that even if I could figure out a way to rig it, there would be too much resistance. Any ideas?

Is there a way to add back-up battery power? I am cautious of power outages resetting my cage's cycle inopportunely.

Do I have enough pins to run all of this? The LCD is 7 pins, and I presume 1 per button, relay, and motor... by my count that is 13, and the BBB has "20 general purpose I/O pins".

Thank you in advance, and of course any general advice you could offer a cost-conscious newcomer would be greatly appreciated!

a automotive windshield washer pump would work and would be easy toggle with a relay. these can be had new for like $20. add a proper mist nozzle to the output and you should be set.

ultrasonic misters are pretty common nowadays. they are used as household humidifiers, halloween/ambient effects, water purifiers.

any computer UPS should work. for added efficiency, you can skip the wallwart and power your electronics directly from the 12v battery inside the UPS. a fuse on the output from the battery is always a good idea.

you can use a $0.75 shift register to reduce the pin count for the lcd from 6 to 2 pins. Google Code Archive - Long-term storage for Google Code Project Hosting.

if it were my project/pet, i would opt for a god bit of redundancy in the system. he'll probably be ok if the mister gets stuck in the on position, but if the heater malfunctions... probably not good! you could limit the current available to the heater so if the relay or µC were to latch on permanently, the temp would top out at an acceptable level. alarms via LED and/or buzzer, email, sms, redundant sensors, etc.
cheers!
-sj