Torch
The torch upgrade is your light source, and is helps you see further in the dark mine. You will start with a candle, which is good enough to get around, but it will only get you so far when you're hunting for rare ore.
When it comes to light sources, the brighter the better! Brighter light sources give you a much larger light radius. They'll pay for themselves over time in the exploration time savings.
You won't need to worry about your light source above ground, exploring in town or up in the snow. These areas are naturally lighted, and you'll be able to see regardless of which light source you have.
The third tier Torch upgrade is the lantern, and it will get you quite a lot of light. However, after you purchase it, you'll find there are even brighter lantern upgrades if you can find the items to use to enhance your lantern. Keep your eye out for light-related items that may be able to brighten up your lantern.