I do a lot of monitoring and use temperature and electrical power (all electric house) dataloggers. Weather data can usually be found for whatever area you are in the country. You have to decide what you actually want to find out, this will make choosing the right kit easier. The second part is analysing the data (you may have a lot of it), that can be a bit tricky if you are not used to doing it.
Main thing is to get stand alone loggers that can transfer the data to a PC. I used a HOBO logger when I was doing some research work and that was a good bit of equipment but quite costly, but did allow for many different types of sensors to be plugged in.