If i was you i would just buy a new power supply first and gain up to a much higher end graphic card. There is not many good graphic cards if you are using a 300 watt power supply. But my first build was about 3 years ago i used a 300 watt power supply and i had a Nvidia GT 520, that card can run Battlefield 3 on low with about 30 fps and that card recommends about a 300 watt power supply. If your not playing any high detailed games like Battlefield 3 and just surfing the internet or play games like Call of Duty i would recommend a Nvidia gt 520 if you are going to use a 300 watt power supply.
Is the Diamond 6450PE31G Radeon HD 6450 Video Card also a suitable alternative to the NVidia GT 520 with the 300 watt power supply. I am not a gamer. Need to read map details, weather cloud details and such.... kaceltd
On a 300 Watt PSU the best card you can get right now is the Radeon HD 7750. It performs decently in games, much better than the GT 520 listed above. There is also the Radeon HD 6670, which is a bit slower than the 7750, but also doesn't need a lot of power. The cards below those two aren't really worth considering if you are gaming unless you are on an extremely tight budget. Even then, I wouldn't go below the Radeon HD 6570, the cards below it are generally abysmal for gaming.
As for nvidia options, there really aren't any really good nvidia options that are cheap, and can run on a 300 Watt PSU. Nvidia doesn't seem to be seriously competing on the low end anymore. The only current gen offering on the low end from nvidia is the GT 640, and it's overpriced for how it performs. Aside from the 640 there is the 520, but that card is only barely adequate at best for low resolution gaming. The GT 440 might also be worth considering, if you can find one, I think they have been discontinued, and it's only worth it if you can get it cheaper than the 6670, as the 440 is a bit slower than the 6670 is.
Edit: If you're not gaming, just get a 6450 or GT 520, it really doesn't matter. 2D performance on either card is the same, just get whichever one is cheaper.