A bigger power supply, such as a 500watt (as jldevoy suggested) would be a good option, however that depends on the components in your computer, and future upgrade plans. But as a general rule of advice if your upgrading from 250watt to 500watt that would be a good upgrade, and no a bigger power supply will do absolutely no damage to your system, as long as it is of good quality. A good quality power supply is essential to having a reliable system. A bad/cheap/unknown brand power supply can damage your system as they are not reliable, and have various problems.
Whats your budget for the new power supply? I would go with a brand such as corsair, seasonic, or antec, they are of very good quality.
Hope this helped!