I know that to run this emulator, Im gonna need a good CPU. Im currently trying to put together a ~$500 gaming PC build. Would an i3 be good enough for emulating Wii games? Could I go lower? Or do I need something better than an i3?
You don't NEED something better, but you'll want something better for most games.
If you're planning on running things in HD with constant frame rates, you'll probably need something a bit better, at least for some games.