Just as a note- there is a chance that you can't unlock the 4th core, but I'm currently 3 for 3 in unlocking AMD cores (2 Athlon II x3's to x4s and a Sempron x1 to an x2). Seems like the probability of unlocking is pretty good with the Athlon II series (Sempron is still a crippled Athlon II).
For the things that you do, onboard video will be just fine- no reason to use the 7300 as performance-wise, both will do what you need, but the 7300GT add power consumption.