Actually, to get the most out of Dolphin, you should at least have three or more cores. Two for Dolphin's Dual-Core option, and another for LLE on Thread, and LLE audio then should run on its own core. Though I believe your question about what CPU to get was already answered, at least somewhat.
When you say talk about this upgrade for Dolphin, you are talking about your laptop right? Like I said, I don't know how easy (or feasible) it is to upgrade the CPU in laptops. For desktops though, you have lots of options. If you want a good dual-core CPU for Dolphin, the i3-2100 is low enough in price, and it performs very well on a lot of games. Another cheap Sandy Bridge chip is the Pentium G860 and that handles most games fine. The i5-2500K, as previously said, will handle almost anything Dolphin can offer, with some overclocking of course.
Your settings look fine for the most part, except you should make sure the bottleneck here isn't your GPU. Try setting your internal resolution to 1x, and turn off all anti-aliasing. If you get speed boost, then that means your system is being limited by your GPU. If the frame rate and game speed stay the same, then your CPU is the bottleneck.
When you say talk about this upgrade for Dolphin, you are talking about your laptop right? Like I said, I don't know how easy (or feasible) it is to upgrade the CPU in laptops. For desktops though, you have lots of options. If you want a good dual-core CPU for Dolphin, the i3-2100 is low enough in price, and it performs very well on a lot of games. Another cheap Sandy Bridge chip is the Pentium G860 and that handles most games fine. The i5-2500K, as previously said, will handle almost anything Dolphin can offer, with some overclocking of course.
Your settings look fine for the most part, except you should make sure the bottleneck here isn't your GPU. Try setting your internal resolution to 1x, and turn off all anti-aliasing. If you get speed boost, then that means your system is being limited by your GPU. If the frame rate and game speed stay the same, then your CPU is the bottleneck.