You are going to be unable to run this emulator on your current specifications, at least not at playable speeds. In the end an actual Wii and games will cost you much less than buying a PC that can play Dolphin somewhat decently.
Note that Dolphin is still far from complete, compatibility is still quite low, most games crash or have graphical problems and it is not yet a viable alternative to the actual system. In the end the actual system and games will give you much less of a headache.
When your ready to be serious by not spamming and want recommendations on hardware for a new system if you opt to still use Dolphin, the Hardware Discussion forum would be more appropriate: