Lots to choose from, but here's 3 suggestions:
Radeon X1650 Pro ($40)
Radeon HD 4670 ($80)
Radeon HD 3850 ($100)
Installation is easy, so no need to worry about that. Since you already have a graphics card in you can open the case, release the tag on the old card, pull it out and insert the new card.
A 300 watt PSU may be enough to run a higer powered card providing its marked and tested to high (running) temps. A generic brand may struggle.