Absolute beginner..How do I get started?

The project sounds eminently suitable for an arduino. The only thing to be careful about is the number of pins you need. If you choose your sensors with care, an Uno would be sufficient, but you'd need to make sure you're using at least some sensors that can share. Measuring temperatures with some DS18B20s is an example - if they cover the range you need. Similarly, common LCD panels require a lot of pins, but there are serial versions that only need two. Then there's external multiplexing hardware, or you can just throw cash at the project and use a Mega.