An Athlon II or Phenom II would be a huge improvement over a Sempron. Athlon II is a lower grade than Phenom and personally I would recommend at least a Dual Core Phenom II for everyday tasks and a Quad Core Phenom II for gaming, rendering, etc.
OP, take a look at the motherboard front panel connector area inside your case. Is it a single connector or multiple ones? If it is multiple ones, you could easily upgrade your board and CPU with another motherboard of the same form factor. I have an old P4 emachines case like that and it is currently equipped with a Phenom II X2, 4gb ddr3, and an old HD 3870. I use it to watch netflix on my old 27" TV.