How to browse available payment extensions?
When it comes to selecting a suiting payment processors I would recommend having a look at this page.

Also, make sure to read any documentation you can find on those payment processors intersting to you, such as:


Developers Website
Extension's Githup Page
CiviCRM Wiki
...


Make sure it is compatible with your version of CiviCRM and does not have major bugs that prevent you from using it.