Is there any alternative to OpCache? I have a hosting with suPHP handler which doesn't support opcache. I want to start working on Drupal 8 sites which highly recommend opcache. 

Is there any alternative to opcache? Should I change my hosting?
Any properly configured opcode cache should work. Notice that Drupal only currently checks for PHP Opcache in its requirements. Some people have got Drupal 8 working with XCache, for example.

APC is really not the way to go. It exists in a backwards-compatible way in PHP 5.5 and as a token-based data cache (still useful, but it isn't an opcode cache in that configuration).