How to connect Arduino to Database?

I want the database update the data each time they count up, then which database can I use:
a. Microsoft Office Access?, or
b. SQL database?
c. Visual Basic?

Visual Basic is not a relational database. It is a programming language. Neither Access nor SQL Server have mechanisms to read from a serial port, so you will need to create an application that can read from the serial port and store the data in the database.

I prefer to use Visual Basic, if I can use it, then how to connect it to my Arduino UNO?

See above.

Is there any example how to make the database?

There are plenty of books - online and dead tree versions - that delve into creating databases. There is nothing Arduino-specific about your database.