Depending on what games you plan to emulate on Dolphin, you don't necessarily need a gaming computer. In your case, you should ideally get a new computer regardless if it's a gaming PC or not, if you're looking to play Dolphin at decent speeds.
Unfortunately, you can't just "give up" certain graphical aspects to improve performance. You can lower the resolution (the Internal Resolution) and Anti-Aliasing to reduce the load on your GPU, but if your CPU is the limiting factor of your performance, Dolphin will still encounter CPU-based slowdowns.
Your CPU was very weak when it came out, and it's severely outdated now. For Dolphin, it's not much good except for very light games (Animal Crossing, Bomberman Blast, Muramasa: The Demon Blade). Ideally, you should consider a budget and the games you want to play, then we can help you pick out hardware from there.
Unfortunately, you can't just "give up" certain graphical aspects to improve performance. You can lower the resolution (the Internal Resolution) and Anti-Aliasing to reduce the load on your GPU, but if your CPU is the limiting factor of your performance, Dolphin will still encounter CPU-based slowdowns.
Your CPU was very weak when it came out, and it's severely outdated now. For Dolphin, it's not much good except for very light games (Animal Crossing, Bomberman Blast, Muramasa: The Demon Blade). Ideally, you should consider a budget and the games you want to play, then we can help you pick out hardware from there.