There are two main types of databases. The smaller business ones like Microsoft Access or the more industrial strength ones like Oracle or Microsoft SQL.
If you are a bit switched on with IT, you can probably learn to program Access or even Oracle or SQL or a very good freebie called MYSQL, but for most people, they will buy an application that uses a database to store the data in.
If you have a choice and you have a reasonable sort of server or high end PC you are going to run things on, look at going for the industrial strength option. A lot of applications have what they call a "Run time" version of the industrial strength database. This allows you, for example, to run a cutdown SQL database as your database. This is more stable, has better user access and most importantly, is scalable, so in a few years time, you won't have to pay $10,000 to have your Access database converted to SQL.
Don't get me wrong, MS Access and many other small database applications are great, but they have limited ability to scale, which can cost you big money and lots of down time in the future. If you have the choice, go for the industrial strength run time database.
If you're database comes with log files, you should put the log files on one physical drive (see link on hardware) and the database on another physical drive. This speeds up the database, but most importantly, provides up to the second data recovery if only one physical drive crashes (at least in theory).
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