So I had my charger installed a month ago while waiting for my Model 3, in York Region.
So a few things to consider:
a) I have a double car garage and I have 2 cars, so the Model 3 will be inside
b) My elec panel is in the garage, so the run to the charger is very short
c) I wanted to future proof a bit, in that once my 4 year lease is up, I don't know what new electric vehicle may be next
d) My elec coming to the house is 100A, and I had breaker spots free on my elec panel. So no extra items needed from this front.
Therefore, in the end my specific set up was a NEMA 14-50 plug installed by an electrician, with a run of about 10 feet from the elec box. This will then allow me to use my mobile charger that comes with the car so I don't have to buy another charger, except the 14-50 adapter for it. Since I have a SR+, it only charges max 32A off AC anyway, and that is the max output of the mobile charger v2 anyway.
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Costs are highly dependant on where your panel is, how much incoming elec service you have to your home, how much elec overhead room you have left on your panel in both capacity of elec, and capacity of spots for breakers, how long the run to the end point is, and whether it needs exterior proofing etc. You should really look up electricians and get quotes, as only they can tell you what it is going to be for your specific situation.
Tesla's own website has a bunch of contractors already, and a google web search will net you more. I got 3 different quotes, and went with the one that I thought was the best and not overtly expensive.
All the contractors wanted a description of your car, and pictures of the spot where you want the endpoint to be, as well as detailed pictures of the panel and the run to the endpoint. This will help them quote you accurately.
Good contractors will also insist on an inspection afterward, which you will have to pay 75 bucks for to get a sticker. I got one cause I don't want insurance issues later.
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In your situation, you will definitely need to weather proof the endpoint, whether it be a plug or not. The Tesla Wall Charger v3 is already weather proof, so at least there that, but for a SR+ the extra charging speed that a wall charger can provide is wasted (if you have the elec capacity, the wall charger can charge up to 48A which is 80% on a 60A circuit, while a SR+ only does max 32A). The mobile charger v2 from what I understand is also weather proof, just don't put it in a puddle... (but you should research more on this, as in my application is indoor I didn't look into this a lot)