Windows asks if what I am plugging in is a headphone or "speaker out".
I would have expected you had three options, not the two that you mentioned: "headset", "headphones", and "speaker out". The "headset" option should let you record sound, but...
Like many laptops, according to this page https://www.asus.com/sg/Notebooks/UX51VZ/specifications/ your ASUS UX51 has a "combo audio socket". This is not really intended for what you want to do. The fundamental problem is that the computer can't both record and play back sounds through the one audio socket, so at best you would be continually swapping the plugs between your Casio keyboard to record, and your headphones or speakers when checking the recording you made with Audacity.
The cheapest option would be to get a simple "USB audio adaptor" like this one: https://www.scan.co.uk/products/dynamode-external-usb2-sound-card-20-adaptor-(usb-stick)-pc-mac
Note, this is not a recommendation for this specific device (I've never used it) - it's just an example of what these adapters look like, i.e. a "thumb drive plus some audio connectors". There are many similar devices available in the same price range.
That plugs into a USB port and gives you two sockets for "microphone in" and "headphones out". Audacity should recognise it as two Audio devices, one for input and one for output.
There are many similar devices for sale, and some only provide audio out (for example 7-channel surround sound) so make sure you get one that has an audio input socket - and if you don't need surround sound output, don't pay extra for something you will never use!
If you get serious about recordings, you would probably want to upgrade to a USB audio interface (not adapter) but that would be in a price range of say $100 and upwards, rather than $10 for a "get you started" adapter.