From what I understand you can use a custom domain on the personal/family plans, but if you're aliasing emails (e.g. info@yourdomain, notify@yourdomain) to a single address, you need the business plans.
Offically you can only use the Family account on a custom domain register with GoDaddy, there are a few hacks out there to get around this but they could be broken at any time
I haven't actually switched it yet so I can't confirm that it works, but the option is there.