It is recommended to use either the MySQLi or PDO extensions. It is not recommended to use the old mysql extension for new development, as it was deprecated in PHP 5.5.0 and was removed in PHP 7.
PHP offers three different APIs to connect to MySQL. Below we show the APIs provided by the mysql, mysqli, and PDO extensions. Each code snippet creates a connection to a MySQL server running on "example.com" using the username "username" and the password "password". And a query is run to greet the user.
Example #1 Comparing the three MySQL APIs
<?php
// mysqli
$mysqli = new mysqli("example.com", "username", "password", "database");
$result = $mysqli->query("SELECT 'Hello, dear MySQL user!' AS _message FROM DUAL");
$row = $result->fetch_assoc();
echo htmlentities($row['_message']);
// PDO
$pdo = new PDO('mysql:host=example.com;dbname=database', 'username', 'password');
$statement = $pdo->query("SELECT 'Hello, dear MySQL user!' AS _message FROM DUAL");
$row = $statement->fetch(PDO::FETCH_ASSOC);
echo htmlentities($row['_message']);
// mysql
$c = mysql_connect("example.com", "username", "password");
mysql_select_db("database");
$result = mysql_query("SELECT 'Hello, dear MySQL user!' AS _message FROM DUAL");
$row = mysql_fetch_assoc($result);
echo htmlentities($row['_message']);
?>
I suggest you try out both MySQLi and PDO and find out what API design you prefer.
Read Choosing an API and Why shouldn't I use mysql_* functions in PHP?