There are no direct flights from India and you can use any of the Schengen countries as a stop. Traveling through UK requires a special transit visa unless you already have an entry visa for UK therefore avoid UK. Some suggested connections to Reykjavik include Paris, Copenhagen, Amsterdam, Oslo, Frankfurt, Stockholm and Helsinki. Multiple layover flights will be cheaper and cost around INR 50000 - 60000.
Two airports are present in Reykjavik, one for domestic and the other for international flights. Keflavic International Airport serves as the entry point for most travellers and is located around 50 km southwest of Reykjavik. Icelandair is the major carrier that supports flights from various parts of Europe and North America. WowAir is another carrier with similar cities of origin. To get to the Reykjavik city centre from the airport you can use private taxis, public bus transport or private buses that ply regularly from the airport. The Reykjavik airport is the one used for domestic flights and you can use that if you are reaching there from other parts of Iceland. Air Iceland and Eagle Air are the major carriers.
Cabs are expensive and should be avoided for long distance travel. Renting a car, although easy, might take a hit on your pocket. You can use the Reykjanesbraut to enter the city if coming from the west or the Kelflavic airport. The Ring Road enters the city from both north and east and can be used as per need.
No rail network in Iceland as such.
Straeto is the public bus transport that operates services to various parts of Iceland. They have an excellent website/app and scheduler that makes it easier for travellers to book their local travel. You can also book bus tickets from various private companies that operate in Iceland.
Several cruise ships stop in Reykjavik each summer and usually arrive at Sundahofn which is about 3 km from the city centre. You can visit the website Cruise Iceland to check out different operators that ply cruises to Reykjavik.