To save money, buy helmets at a dept or big box store. You still need to have them try helmets on. You may find close-out deals on helmets at bike shops.

Helmets should fit snug when adjusted properly; too small a helmet will fit too high on the head and probably be too tight somewhere on the skull, too big a helmet will tend to roll forward or back.

You'll need to check your state and local laws -- there may be a cycling advocacy group in your state with a website listing state and community helmet laws. Generally, kids are required to wear helmets, adults no.

Importance for adults...? There's a stickied thread at the top of this forum debating the utility of helmet use. Some think they are critical equipment, and those who don't wear them are ignorant future organ donors; some think they are beyond useless, bordering on dangerous. I wear a helmet to provide some injury mitigation regarding less than serious head injury in the rare occurrence that I crash my bike and the even rarer occasion when I hit my head as a result -- I don't wear one thinking it will make me invincible, a safer rider, or that it will protect me from serious head injury.