Where to store data for module
I'm afraid you need a long answer for this.. 
But using a data*base* to store different values like this is not the best way I guess. 

You can use multiple databases with Drupal and switch them without a problem. But real question would be, why.

However, you can store categories in different table,and refer the category ID from the main sms message table. It's much easier to JOIN queries and get the data you want,rather than having a table for each category. 
Also, I'd suggest using core functionality  when you can. With new entity system in Drupal 7,you can make a new entity, an SMS, and attach fields like category it to.

If you are storing settings of the module, consider using system_settings_form to store settings. You can set/get them using variable_set and variable_get. But make sure that you don't store big text using this. 

Good luck!