I have a web application which provides data analysis service and deployed on Azure virtual machine. How can i publish it on Azure Marketplace and in which category it will fall?
There is a complete and documented process for that.
You first need to apply as a certified partner : https://azure.microsoft.com/en-us/marketplace/programs/certified/
Then in the publish steps you will choose up to five categories : https://azure.microsoft.com/en-us/documentation/articles/marketplace-publishing-push-to-staging/#step-4-choose-azure-marketplace-categories
Same thing for all marketing info (logos, pricing, ...)