How to reduce first byte time

[GreenGecko]

Additional things you can try:

1. Move the server to be as close as possible to your target audience ( and use a decent VPS provider: there is a huge variation! ).
2. Enable all available caching. Apart from Wordpress plugins like W3-Cache, this includes Opcode cache ( APC or Zend if on PHP 5.5 ) and all relevant database caches. THe intention is to be able to feed the website from memory and avoid disk when possible... always slow, but often really, really slow on VPSes
3. Ensure latest WordPress, PHP, and if seriously after every millisecond look at using Percona Mysql 5.6.
4. Replace Apache with a lighweight web server like nginx

After that it gets more difficult. A code review is always good: as you've seen not all plugins are created equal. Also, the pagespeed web server plugin from google can help patch over poor quality code, but it does further complicate site maintenance.