I want to buy/subscribe to salesforce edition. I need to have a connected app that I will use for authenticating salesforce users on my third party webapp. The only reason I want to subscribe to salesforce is just to create a connected app. What are my options?
You can create a Developer Edition and park a Managed Package there with your Connected App. You only need a paid edition if you want to use it for your business (e.g. marketing/sales/support) as well as your LMO (License Management Org). There's no need to pay just to have a Connected App. Just remember to meet the minimum qualifications to avoid being marked inactive and deleted.
Connected Apps can be created in: Group, Professional, Enterprise, Essentials, Performance, Unlimited, and Developer Editions
Connected Apps can be installed in: All Editions
A connected app is one thing, but to make it useful you probably want to be able to write Apex (the Salesforce proprietary, java-like OOP language). In which case you need at least the "Enterprise" edition.