Your description of usage suggests that SQL Server Compact 4 would be sufficient for your usage. Your scenario is generally the reason SQL Compact was created. If you don't already have a full SQL Server instance at the ready, then consider choosing the SQL Compact solution.
It sounds like the advice given was focused on 'heavy-duty'. I'd consider heavy-duty to be sustained reads and writes, or requiring features not in SQL Compact: stored procedures, procedural TSQL, replication. See more on feature sets of SQL CE 4 & SQL Server 2008. Obvious advice would be to pick the engine that your web app needs.
The great thing about SQL Compact is that you can scale up/migrate to a SQL Server instance without much effort if/when your requirements change.