CPL + IR + Multi rating + MCC = fATPL
So, CPL and IR (which are two separate flying courses of 25 and 50 hours respectively, if done in that order) takes you most of the way to fATPL. You will usually do the Multi Rating (6 hours minimum) and CPL before the IR as having the CPL gives you 5 hours off the IR (otherwise its 55 hours) and if you want to get a fATPL you will want to do the multi IR, as that is what airlines will obviously want.
You don't need an IR to be a flying instructor but you do need an Instructor rating, which is another 30 hour course. Work with only a CPL will otherwise be very limited. In theory you can do aerial work which does not require transport of passengers, but in practice...... You could do pleasure flights but only if employed by a suitable organisation with the appropriate Air Operators' Certificate.
<<edit: The Flying Instructor course is 150 hours - 30 hours of flying, yes - but a 120 hours of groundschool. I comment only for thoughts of budget, both financial and time. Done properly, the 120 hours of groundschool will take an extra three to four weeks of classroom time and will need to be paid for.>>