Hi
Take a look at speakev.com/categories/mitsubishi-ev-forum.128/
The Outlander should come with a 5 metre special cable with a standard 13 amp plug on the end. It can charge with that from any decent outside socket. I have a Leaf and at home I charge it with the equivalent cable from the outside socket we put in for the lawnmower. A full charge from empty, according to Mitsubishi, takes 5 hours. If the car doesn't have this cable I would be suggesting to the dealer that they should be replacing it.
The Outlander has two charging sockets. They are a Type 1 and a ChaDeMo. Both are Japanese standards, as you might expect -- the European standard is Type 2. The standard 13 amp cable goes into the Type 1 socket. The ChaDeMo socket is only used with what are called 'rapid' chargers of the kind you find at Motorway Service Stations, IKEA and some hotels.
A dedicated home charger will have its own circuit off the fusebox. It can either be 16 amp (which is around the usual power of a power circuit in the house) or 32 amp. However, current Outlanders can only charge at 16 amp (taking about 3.5 hours empty to full), so there is no immediate need for 32 amp, though going for 32 amp may provide some future-proofing as this is becoming the standard on the latest electric cars.
A tethered charger is one which has a cable built-in, so you simply unwind it and plug it into the car. For an Outlander, a tethered charger would need a Type 1 plug to match the Type 1 socket. The disadvantage to installing one is that Type 1 plugs and sockets are being phased out in Europe, and future electric cars are going to have Type 2, so if and when you change the car you would also have to change the charger.
An untethered charger will simply come with a Type 2 socket and you will need a cable with a Type 2 plug at one end and a Type 1 at the other to use it. That is a little less convenient as it means plugging in at both ends, but has the big advantage that most public charging points have Type 2 sockets, so you can keep the cable in the boot and charge away from home. It's more future-proof since a Type 2 car can also charge using a Type 2 - Type 2 cable and has the advantage that, should the need arise, it is easier for other cars to be charged there.
Mitsuibishi do not include a Type 2 - Type 1 cable as standard but these can be bought from various suppliers, not just a Mitsubishi dealer, and probably cost around £125. A lot depends on how you will use the car, but I would probably go for an untethered and cabled solution. I'm afraid I have no experience with Rolec.
If you have solar panels there are further considerations, but I won't set them out just now!