A PSU does not supply 100% of its labelled wattage 100% of the time.
It only provides whatever the system needs at any given time with some power loss due to the AC to DC power conversion inefficiency.
If your system is drawing 300 Watts and we assume an 82% conversion efficiency for the 600 Watt PSU @ 50% load then you should be able to measure the power draw at the PSU's AC power plug as being 366 Watts.
You can safely use any wattage of a PSU, but you don't want to get too big of a supply from an efficiency standpoint. If you are drawing less than 20% of the PSU's capacity the efficiency starts to drop off a cliff and you will draw more at the outlet. It will work, but basically will cost you more on your power bill. If you are running a 300Watt and you want to put a dedicated video card in there a good (emphasis on quality here) 500Watt or 650 Watt would be fine. The Antec Earthwatts Green line are decent quality and relatively cheap. If you are not looking to add a graphics card, shoot for the 500Watt: