Best way to get SQL Server databases on small capacity VPS
SQL Server Express Edition is limited to 10GB maximum database size (per database) and 1.4GB of buffer pool memory per instance, so you won't "kill" the server by running it if there's nothing else (or very little) running on it. However, if you're doing a lot of work with the database(s), you'll find yourself starved for memory and reading a lot of data from disk instead of caching in memory.

Bandwidth? That depends greatly on how much traffic you'll have going into &amp; out of the server.


  I wasn't able to find anyone who cost effectively would rent me just some space on a SQL Server database.


Azure SQL Database is very similar to what you describe here. "Cost effective" is in the eye of the beholder.