For the technical part: Yes the client must be running 24/7, and yes your ntp_time_error is a problem. You need to install an ntp daemon that will keep your computer's time synchronized and correct. On Ubuntu this can be done by installing the ntp service: sudo apt-get install ntp. Btw I don't think it's recommended to run a delegate via the GUI, the best way to do it is via the command line interface using Linux on a VPS.
As for moving up the list, you will need people to vote for you, and for that you need to market yourself. You can provide a service such as a blog promoting Bitshares for example, but basically you need to provide a reason for people to vote for you.