Re: How do I get my app featured in Azure Marketplace?
The shortest, best answer is: grow the usage of your app through Marketplace!
For VM-based apps, encourage your customers to deploy through the marketplace. As they deploy and grow, so will your presence in the Azure Marketplace.
For "contact me" or trial listings, consider campaigns to drive more traffic to your listing to increase the leads and trials that are being sent or used through your offer.
All Azure Marketplace publishers are able to access category-specific promotions through the go-to-market benefits that are provded once you go live (or if you update an existing offer), so that's a good place to start.
In general, the Azure Marketplace team is measuring the growth of your app in marketplace, traffic to your offer, ratings and reviews, and special consideration for offers that are clear, informative, and include good visuals in the screenshots section.
Please note that featured apps are different from the "preferred solution" icon.