We are traveling to India in March and April 2017. We want to arrange to have a driver pick us up at the airport and drive us to our hotel. We also want to hire a driver to take us to various sites in Varanasi, Mumbai, and Kolkata. We also need someone to drive us from New Delhli to Amritsar and then from New Delhi to Agar and Jaipur. Is there an auto driver company or tourist agency that can connect us to a trustworthy driver?
You can check some online taxi operator i.e carhire.com, localtaxiibooking.com. You can take quotation from couple of more online operators and then go ahead.
Drive from new Delhi to Amritsar is not advisable . Its very long and you wont be able to cover it in a day. It is better to take flight or train from Delhi. There are some good trains on this sector.
You can take local driver in each city. Delhi, Agra and jaipur can be covered by one driver as well.