Sounds like you already bought the replacement, but I would have suggested a used 18-70 as it's arguably a better lens and can be had for cheap. That's if your only goal was to straight replace the broken lens.
You'll definitely want to study up on f/stop, iso, and shutter speed to get the basic concepts of photography and allow you to make more informed decisions regarding lenses and what they can do for you.
Once those concepts are solid, you'll want to figure out what sort of shots you'd want to capture that you aren't able to get with the stock lens (low light, wide angle, quality telephoto, macro etc). Then you can target your search on lenses that will help you get those shots you weren't able to get. Who knows, your search may even direct you to a flash/speedlight to get the shots you want over a lens.
Then, if you really want to, you can read up on lens technologies (not necessarily MFT graphs) to understand what makes a lens "worth" $1k or more. This isn't particularly required to make buying decisions on lenses.