Super cheap Azure SQL Database
If you're looking for a super simple, super cheap SQL Server database, for basic development or for a very lightly used production application, Azure offers their "Basic" instance for about $5 per month. It's extremely limited, but if you're looking to spare every dime, it'll function.
Developing .NET on a Mac or a cloud IDE means you don't have access to a local SQL Server instance. This kind of thing may suit your needs. And if it doesn't, you're only out a tiny amount of money.