The best graphics card you can install with a 300w PSU is either the Radeon HD 7750 or the GTX 650. The GTX 650 a little more powerful (by 8% ??), but since they are lots of rebates for Radeon HD 7750 card flying around, I have seen a HD 7750 1GB DDR5 card selling for as low as $65 - $70.
These are mainstream cards. Much better than the Intel HD 4000, but they will not let you max out graphics on a 1080p monitor unless of course it's an older game with relatively lower requirements than current games. At best I think you can get good performance for most games using medium quality graphics at 1080p resolution.
Your budget will determine what you can upgrade to.