If you are just a startup then MailChimp will work best for you. They provide lifetime free plans for 2000 subscribers and you can send upto 12000 mails every month. Other provider i would recommend is Mailigen. Click here for more details on the best Email Service provider.
Also, it is always recommended to use a clean email list before sending a campaign as high bounce back rate can lead to negative impact on your domain/IP reputation. Use email cleansing service to remove invalid emails from your list.