People tend to have their favourites. Personally, I greatly prefer PostgreSQL as it gives me much less pain than MySQL does. I'm certain others will disagree with me.
What matters is your requirements, preferences, etc. I strongly recommend trying things out for yourself to pick what fits your environment.
If it's just to get a feel for SQL, SQLite may be the simplest start as it is contained within a single file. Once you're ready for multiple users, usage over the network, etc. try the documentation and see which choice would make your work easiest.
