It really depends on the type of Business Analyst you want to be - what kind of work you want to do. There are courses and certifications for Business Analysts you can look in to which might be helpful. You may want to give serious consideration to a tool like Crystal Reports, which can connect to any database and generates its own SQL. After all, the point isn't to be a Database Admin, it's to get at data and analyze it.

If you have the option of taking one course in Database Management or Analysis, do it. The basic principles will take you far.

If you really want to learn databases and SQL I would recommend starting with MS SQL Server Express. It's free, relatively easy to use and is well documented.