What board you'll need depends a little on how you want to work I guess.
There is an advantage in having the nr. of pins of the Mega-board. You could easily attach all switches, sensors, circuits for solenoid valves and display.
The smaller board probably has more then enough memory for your program as well though.
Maybe it hasn't enough pins out of the box, but with a few cheap ICs, you could increase the number of IO-pins you need. There are several techniques to do that. With just two wires of your arduino you could control a network of chips using the I2C-protocol for example. That gives you the possibility to just add some more IO-pins, but also to talk with loads of specialized chips.
Using 3 pins you could work with shift-registers, one will give you 8 I or O pins. The beauty is that you can daisy chain them, the first chip driving the second and the second one driving the third. By placing 20 in a row, you could control 160 pins using just 3 pins on the arduino.
A third method might be using the 1-wire protocol. That also makes it possible to talk with several chips supporting different kinds of functions using just one pin. The number/functions of chips isn't as large as I2C-chips, but it's better at long distances. With a 1-wire temperature sensor and IO-chip in each room... you might be able to control the whole house with just one pin.
Disadvantage may be... that you'll have to know how to drive those chips and read a lot of data-sheet before... you can start/finish a full size project.
For me discovering and getting all kinds of chips/technologies working is what makes the hobby a challenge. Starting a first project, maybe having to spend loads... of time to get it working, can be frustrating though.
One advantage of the Uno (/DIP-based arduino) is... the easily replaced micro controller. Should you accidentally ruin the chip of a Mega-board, you'll have quite a lot of work to replace the chip and maybe even need a new board.
If you already got some electronics laying around, I'd just buy board, LCD-display and components needed. Starter kits with things like buzzers, a number of leds, resistors, light-sensors etc do give the absolute beginner in electronics some possibility to experiment, but if you already know a little I wouldn't spend the money.
The LCD could be a text-based or graphical based one. I'd go for an text-LCD based on the HD44780-chip. Those are probably most used by arduinoists and are available in several sizes, 2x16 characters, 2x20, 4x20 and other formats...
It's not easy to tell you what you could use best, since there are many ways to create what you want.
I hope I haven't made your choice more difficult sofar