I am looking for a graphics card to be able to play higher graphic based games and need any advice on if there are any that would work and would be compatible with my pc. My PC's Specs are linked in the following gyazo links. :
I assuming you have like a 300w powersupply, if so that card will probably be the max you can support. It does not require any pcie power connectors to run. The card is low profile so it should fit in your case
you could always go the HD 7750 route. It is the most powerful card that doesnt need extra power. It uses 5 less watts than the 430 and has a ton more power than the 430, but it is more expensive, though it looks like the site has lots of different ones at various prices. I would stick with the first 2. The second is just clocked a little faster, not quite sure if it warrants the more money.