Usually you're limited by what your hosting provider uses, or what your company already users / is willing to support, so those are your first considerations.
MySQL and PostgreSQL are the ones you usually see for smaller setups, because they're free and most hosts offer at least MySQL.
MS SQL Server is expensive, and tied to the Microsoft platform.
Oracle is even more expensive, but much more of a true database and more feature-rich than any of the others.
If you want major differences, Google for 'database comparisons' or some such. They all use SQL, just it depends on what extend sometimes and the extensions they offer as well. Stored procedures and triggers are a whole 'nother can of worms.