I am a SQL Server DBA - I am biased towards SQL Server. However if the budget is limited, I would suggest trying a mature open source database, perhaps MySQL, PostGreSQL or MariaDB.
Performance isn't your real issue here. The security of your data and the safety of strong ACID transactions are what you should really prioritise. How are you going to backup your data with SQL Server Compact? Do you intend to replicate your data to a reporting database? What if your instance of SQL Server Compact goes down, can you provide high availability?
The other enormous advantage of PostgreSQL and MySQL is the huge community of people using these and willing to share their knowledge / experience. We have this in SQL Server as well, but not with SQL Server Compact :(