Speeding up word presds websites

We have two Website in wordpress with loads of plugins needs speeding up (has to be fast on all browser/OS combinations including linux and all mobile) whilst remaining editable -the job is to advise our developer exactly how to do this as we are continually working on the site and adding things which slows it down . We also have a plugin for an online chat facility that is required to be plugged in to one of the websites.

We also require some other things which I will detail and add in private when we discuss the job specification