I have little to add about tracking it, but will comment on the rest.
Regarding the dog crate, make sure it actually fits through the door opening. I have this one in
Small (24") and it
does not fit due to the shape of the opening despite it fitting smaller cars:
https://www.amazon.ca/gp/product/B00QAVNODI/
I also cannot get it into the back for the same reason, the trunk opening is much smaller than the available space.
I have the AWD (non-performance), and it's plenty of fun for me in the mountains. Get ready for some absolutely wild comparisons.
I like driving our 2009 Honda Fit Sport through the twisties. It obviously completely lacks in power, but it's super agile and light. Feels very good through corners. It's a bit wrong how good it feels for this given that is has such low power.
My Honda Crosstour on the other hand made everything less fun. It had way more power (~270hp) but drove like a boat. Completely ruined most sorts of fun on mountain drives, but made highways nicer to deal with. Not fun, but effective.
I bring up this odd context for this reason: The Model 3 is
very heavy, but handles that weight surprisingly well. It feels decidedly
worse than the Honda Fit through corners, but is
amazing for a 4000lb car in my opinion (same weight as the Crosstour was, roughly). Plus it has way, way more acceleration than you can responsibly use on twisty mountain roads anyways -
you'll realistically be limited by the tires more than the available power, especially if the road surface has gravel and such.
Some people have actually reported that the SR+ is nicer for such drives. It has a bit less punch, but still plenty enough and apparently handles much better through corners (probably the reduced weight) with a better steering feel (due to no front motor, presumably).
The one thing I'll note regarding tracking it is the brakes. The stock, non-performance brakes will be completely lacking in a track environment and have been noted by many people in such events. This will depend on the track though, and some people get by just fine (albeit needing more frequent pad replacements than is reasonable).