Of the options, number 2. If contacted prior to landing, I'd notify m immediate supervisor, who is then tasked to make management notifications. Since the emergency has been declared, there will be required notification to the FAA and possibly the NTSB, which usually comes through the DO or designee per the ERP. As dispatcher at a cargo airline, we'll call ahead (depending on how far from the airport they are) to the tower, and send Hazmat info to CFR on field. If it's an airport we have ops, we notify the local station management. If not, the operations people begin lining up ground handling and Maintenance Control starts looking for a local mechanic.
Once safely on the ground, we'll get a quick rundown form the crew on what happened. The necessary official reports will be made by management after the dust settles. The aircraft will need to be gone over by MX in any case. Recovery operations will commence based on the location and severity of the mechanical. In best cases, its a on-line station and we can get another plane there quickly if required. If not, meal and/or hotel vouchers can be issued until the airline is able to move them.
IN the case you presented, a loss of pressurization will not necessarily require an immediately get it on the ground situation, and the crew should have contact dispatch once stabilized at an appropriate altitude. There a joint decision can be made as to the best airport to divert to. For instance if its 15 minutes to Dayton (where you have limited or no service) or 20 minutes to Cincinnati (where you have a hub operation), I'd think about CVG. On the other hand, if the emergency involves smoke, loss of control, or something extremely serious , then the closest strip of concrete you can safely stop the plane on is the call.
Thats the long answer.