Microsoft now offers an Azure image for SQL Server Express:
We just announced that we added images for SQL Server Express with Tools 2014, 2012, and 2008R2 in the Azure Gallery. SQL Server Express is a free version of SQL Server that you can use for dev/test and for web and mobile apps with lightweight relational database needs.
I’m not the world’s biggest fan of Express edition, but if you’re cost-conscious enough, this might be a nice move for you.