The alternative to using the PayPal Website Payments Standard payment method is to use PayPal Website Payments Pro (also known as PayPal Website Payments Advanced). WPP doesn't require your customers to leave your website to make payments. They can pay with PayPal while on your website. As a more advanced service, you will need to have a PayPal Business Account.
You can enable both Website Payments Pro and Website Payments Standard in your store to enable customers to chose their preferred payment method.
Download the Drupal Commerce PayPal module from Drupal.org at http://drupal.org/project/commerce_paypal and install the module on your Drupal Commerce store.
If you need to sign up to PayPal for a business account to make use of Website Payments Pro, do so at http://www.paypal.com.