I chose cgminer.

I'm a bit confused with the settings... 

What is Append JSON conf (-c /var/www/minera/conf/miner_conf.json)?
How should I set the other on/off buttons? (Script, auto login, auto-debug...)

My miner seems to be recognized, but I can't get a hash rate

The installer will configure the system requirements and will tell you the URL to connect to.

Default URL: http://[your-minera-ip]/minera/ Default password: minera

Important: minera system user has password "minera", you should change it if your system is a public host with SSH access.

sudo passwd minera

This isn't the web password, to change the web password, login into the web interface and go to Miner -> Settings

And what exactly are error/rejected rates? 

They are either invalid (bad hash of good data) or stale (good hash of bad data)

When a block is found any share you are working on or submitting is no longer worth anything.  They are stale.   If you push GPU too hard it will make mathematical errors producing invalid hashes.

Thanks a lot for your answers!