Maybe we could start with the basic hardware for the Arduino (I don't even know which one or which kit to get)
There are not that many things you need to be monitoring. I'd start with a UNO. It has 20 IO pins, which should be plenty to get started with, and is not too big or expensive.
a display (if android readouts are too difficult for the beginning)
There are two basic types - character based and graphic based. If you want to just show numbers, character based is fine. If you want to draw pictures, you need a graphic based model.
There are serial displays, which use just one pin, SPI models that connect to the SPI pins (11, 12, and 13 on a UNO), and those that use more pins. Price is generally inversely proportional to the number of pins used.
and some sensors (temperature, hal sensors for speed and crank cadence, maybe a photo sensor to automatically switch on the backlight when it's too dark)
Some of these (the photo sensor is a nice idea) may or may not already be present on your bike. (Perhaps you could tell us about it.)
I think that you'll be happier, in the long run, learning about the Arduino and how to connect it to the bike, of you start with safer projects. Take care, whatever you do.