I would like to create a page that is able to access a database via SQL and return information based on user input. Would it be better to create a page that sends POST information to itself, or use AJAX to interact with the database without using page loads?
Why don't you just use PHP to access the database? There's no need to send a POST request to generate a page using information in a database.
well considering they both do kinda the same thing when interacting with a DB, it just depends if you care the users screen has to refresh or not. so its really your choice.
ajax would be better, less server load, quicker for user, whether you can be bothered or not is another thing.
Just safer overall, no need to show the sql queries to the user.
huh? what language actually shows the queries to the user??
The both system is OK independent for what you need it. For example, if you have some game or gallery, more then one query to SQL and you think the reloads will irritate users then is better to use ajax. If you need only one-two queries (to display user name, birthday, etc.) then it is better to use PHP without Ajax.