Good places to rent a car?

It really depends. Some companies won't let you rent if you are under 25. Others will let you rent if you're over 21 and under 25 but they'll tack on a fee.

As far as insurance, no you don't though you have the option to buy their own coverage in case of an accident. Or you can see if your credit card covers rentals, usually Visa does if you go through the process correctly.

As for companies, I've had good experiences with Avis and Budget. Each time I got a brand new clean car and for half the price as competitors. Though I had someone older than 25 rent it for me so I didn't have to pay the expensive fee.

Enterprise usually has the best price. You need to be 25 and you can buy insurance by the day from the car rental company. You do need a valid drivers license and a valid credit card.

most rental agencies won't rent to anybody under 25

if you don't have insurance, you should buy it from the rental agency - this will substantially raise the fees

how much depends on where and what type of car - NYC, LA will be higher than some remote rural location