I think your H starts with IC and starts to work on his issues. With that is full transparency on his part (obviously). IC for you is if you feel you need it, to deal with the crap that this process brings.
As he goes along, you watch his actions (his words are nothing at this point), and work on healing yourself, and at some point (it's different for everybody), you decide if R is what you want.
Don't pressure yourself to label it, just let the process happen.
As far as finding IC/MC, make some phone calls, see if they have experience dealing with infidelity, get a feel for the practitioners. Maybe your current IC can recommend somebody for MC when the time is right.