Mind posting/linking exact wire, breaker and plug you installed?
You'll definitely want to check a few things to determine what wire and breaker you buy. If your distance from charger to breaker is more than 100ft, I'd really recommend going up a gauge to 4/3 THHN. Additionally, the specific breaker you buy needs to match the manufacturer of your circuit panel. Also, you need to be sure you have "overhead" on the panel, and this does not necessarily mean just having space on the panel to install a 2-place circuit breaker. You need to have amperage overhead as well - if you pull too much power the mains breaker will trip. In my case, I have a commercial-grade Square D Panel so I got a circuit breaker for that.
Most electricians recommend going with the THHN wire which can take a higher constant amperage than your usual NM-B at the same gauge. The electrician who quoted me $2,500 (!!!) was going to use 6/3 THHN wire, so that is what I bought - at this link:
6/3 W/GROUND THHN/PVC POWER TC-ER. I bought 65 ft, and ended up using 55 ft. Will probably use the 10 ft I have leftover to install a 14-50 charger at my vacation house where the run I need is just a couple feet. This THHN cabling is rated to 75 amps, but with a discount from me not totally believing that high rating, you are safe at 60 amps, and the tesla charger will only pull at max 48 amps.
Also, the 6 gauge wires are not color coded. You'll need a multimeter that supports continuity testing, and you should label each wire with a corresponding color on each end (red, white, and you can leave one black).
All in, I spent $150 on the cable, $30 on the circuit breaker, $500 on the charger, and about $15 for cable straps and such. The price on the cable has almost doubled (!!) since I bought it a month or so ago - dang worldwide supply chain collapse! But most people won't need 65' of cable so shouldn't be too bad.
I bought a 60 amp breaker from Home Depot, which is what is required for the Gen 3 HPWC to charge at its max rate of 48 amps (80% of circuit breaker rating). Normally at this high amp rating you need to buy a GFCI circuit breaker, but Tesla specifically says not to do this as the charger has its own GFCI built in.
This video goes through an install and is very good.