@radios
Don't make this overly complicated,
@srs5694 had a spectacularly through answer, and just to maybe distill that down in a few key points for you:
A new M3, here in North America comes with a Tesla Mobile Connector (aka, "charger), and the adapter plug for a standard 120V / 15a, three prong plug, that will charge at 3mi/hr.
You can buy another adapter plugs for the Tesla Mobile Connector for different configuration outlets, that support different power levels, including 240v, and get up to maximum 32a output (~30mi/hr).
NEMA is the specification / standards group that defines those different plug types, and the maximum volts/amps, so you'll see a plug referenced as a NEMA or shorted as N and two numbers, they have specific meaning, but just use the charts linked above in
@EVRider-FL's post.
If you're in a house, it will have the 5-15 outlets (that's the "regular" ones you use all time), and probably a 30a "dryer outlet" of some sort, you can look at the plug configuration, and get a Tesla Mobile Connector adapter for it, that's often times an N10-30, and you see from the chart, that's about 22mi/hr.
You can also get a dedicated circuit and outlet installed, up to 50a, or even get a higher output circuit and hardwire a charger. You should run a charger that's about 20% less than the specified outlet, i.e., a 50a outlet should be used with a charger that supplies no more than 40a.
Which is exactly what we have: a 50a circuit, with a 40a charger, and I just keep my Tesla Mobile Connector stored in the trunk in case I needed on the road, or as a backup if our main one failed. Our "plug style" is an N6-50 (which you'll see is also a TMC adapter plug option).
With our charger we get ~36mi/hr, and it's also compatible with our PHEV Wrangler, it has what's called a J1772 connector on the car side, that's the non-Tesla spec implemented on the Jeep, to use it on my M3, I simply install the small Tesla/J1772 adapter (should've also been in your bag).