there are many ways of configuring mixers and soundcards. Dags has described one way which will work fine.
What you suggest will work fine as well. You don't need to go from your soundcard back into the mixer, and you can send the soundcard output direct to speakers (or an amp and speakers).
My method is not to use the mixer mains as the monitoring output. They go straight into the PC. Instead I feed the PC signal into the control room output of the mixer and hang the monitors off that