Redmine

That depends of the workload you have and the expected size the redmine will have. Put shortly: you have no caching and no write concurrency as in a "real" database, the 2 caveats this brings are: no caching means all accesses go directly to the disk, which might cause high I/O load on the disk if you are accessing redmine with many users at the same time, and no concurrency because a write access to the SQLite will lock the entire file, i.e. during the time it takes for data to be written to disk, nothing else can access the DB. Furthermore, even read performance might degrade with the size of the DB file because of high seek times.

With all that said: SQLite is not a bad database engine per se, but you have to be aware of the limits of the engine. I'd recommend going with PostgreSQL or MySQL if you will regularly have more than 3-5 concurrent users and/or a lot of issue creation, if not, SQLite should work good enough.