Is the mixer digital or analog?

Are the keyboards GM compatible, where you could get all the MIDI sounds from them?
If so, a USB to MIDI adapter so the computer can talk to the keyboard/synth.
These are common and often about $20.

The next question would be how to hook the mixer to the computer so whatever goes in the mixer can be selectively routed to record.

Honestly, in the long run, I think an audio/MIDI interface would be worth the money (instead of the using the mixer as an input) so you can get a good sound from your vocals and the keyboards digitized on the way into the computer (via USB). Better convertors and many more useful reasons in the long run. You could easily move it from location to location and likely find joy.

Focusrite 2i4 would probably be fine for you. I always remind when mentioning Focusrite; the 2i2 does not come with the mixer software applet that allows extra routing options. This adds value to the models above it for many users. When I first learned this the hard way, I decided to warn others.
The 2i2 is the only model without the mixer feature, as far as I know.

Make your sound your own!
.. I do not work here, but the benefits are still awesome