The i3 comes in the USA with what is called an occasional use level 1 EVSE. From empty, it could take up to 20-hours to recharge the i3 with it (the one sold in Europe is a small level 2 unit running on their local supply of 220vac so even at the same amperage, because the voltage is double, the power going in is doubled). Now, if you do not empty the battery in your normal day-to-day use, it might serve as all you need.
There are LOTS of other EVSE's you can purchase. If you want to use the existing 240vac plug, depending on which receptacle it uses and how big of a circuit breaker powers it, would dictate which one you needed, assuming you don't want to install a new dedicated service for the car. To recharge the car at it's fastest EVSE input, you need one running at 240vac and 30A minimum (more would work, but the car won't use it). The car can take up to 7.4Kw/hr into it, and power = volts*amps.
Lots of choices, some plug-in that can get you that full capability, depending on the supply. I opted for a Clipper Creek wired unit, but they also make some plug-in versions. These are entirely made in the USA, which, to me was a plus. There is no need to buy BMW's EVSE unless you like the style or they give you are really big discount - most others are less expensive, and in some cases LOTS less expensive. Basically, the things are generic - all you need is one specified for J1772 use, the plug and signaling protocol the i3 uses.
