Most major rental car companies allow foreign visitors to rent vehicles as long as they have a valid readable un-expired license from their country of residence. If the license is not in English, some rental car companies will require a valid International Drivers License or Permit (IDP) to be presented in conjunction with the valid foreign driver's license. The IDP alone will not be enough to allow you to rent a car.
Some rental agencies will not rent to anyone under the age of 25 or will but charge a higher fee. So if you are below 25, check on the rental car company's restrictions when booking your rental vehicle.
There are some rental companies that have extra restrictions depending on what country you are licensed in. For example Alamo requires drivers with a driver's license from the European Union to produce a license that has been valid for at least the last 12 months. And they require an Irish driver to produce a full driving license and have at least 2 years of continuous driving experience, free from serious endorsement or disqualification prior to rental.
As for insurance, if you do not want to purchase it from the rental agency you can check with your auto insurance company from your home country to see if they will cover a US rental car. You might also check with your credit card company to see if they provide insurance coverage for a USA car rental.
If once you obtain your US license you buy a car, you can then come to us for affordable car insurance.