SocketServer module and SQLite

So I have to make a small website for internal use at work (my work is not related to programming). And since our office is about 200 people I thought that I'd use the SocketServer module with SQLite database and this way I am going to learn some new stuff. From what I see the only way to do it is to connect to the database at every request. Isn't that expensive ? What happens if 2 people send requests and try to connect to the database at the same time (or close) ? So I have :

1. Start the server
2. At every request the server initializes RequestHandler instance and then I have to connect to the database ?

I am not posting code because its a general question of how the process works.