Not an expert but...
Using a standard 120v outlet you can get ~4 miles per hour charge, which is 32 miles if you leave it plugged in for 8 hours overnight. This is definitely the most frugal option in terms of installation.
Installing a NEMA 14/50 will get you in the neighborhood of 20 miles per hour charge - we don't yet know the max amperage the M3 can charge at. Older Model S's could charge at 40 or 80 amps (if dual chargers were installed), newer ones can do 48 or 72 depending on if you got the charger upgrade. The speculation is that the M3 will either match the 48A on the MS, or be somewhere in the 30A range. Regardless, with your situation the NEMA 14/50 should provide more than enough charge. The only downside is that you will need to use your mobile charging cable, and either leave it in your garage if you don't plan on needing it on the go, or roll it back up and put it in your trunk each time you're done using it (or buy a second one).
The HPWC (high power wall charger) is the least frugal option but gives you the most flexibility in terms of input amperage and future Tesla purchases, and also means you can keep your mobile charger in your car (you know, for actual mobile charging
).