I'm buying a car and garaging it until I can fix it. Do I need to have insurance on it to be able to register it (so I won't get fined for not registering it) or can I just register it like that since I won't be driving it for a few months?
Mandatory insurance is required for registration. But the requirements are for liability insurance. You may submit affidavit of non-use and will not be required to have insurance (at least that's how I understand it).
Registration is required within 60 days, not 30 (same link as above).
Insurance for the damage or loss to your car - up to you. If you don't care if it gets stolen or burns with your house or gets damaged when a rodent eats through the tires while you're not watching - then don't get insurance. Keep in mind, that if for some reason the breaks fail, the garage door gives in, and the car rolls out on to the street and causes damage/casualties - it will be on you.