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I am not a huge fan of any Automatic transmission.
as for beginner track training. Wouldn't consider an Auto of any kind, but that's just me. Is the old 3 speed auto tough enough? I would really think so. If all the computer control's are still working properly on this 81. Could be fun.
Me, I'd still look for a manual car.
you Drive a Manual, you ride in an Auto.
The aluminum Dana differential is more likely to be the weak link in the 80 through 82 cars. Save your pennies, and do an iron differential conversion (with the batwing) when the differential breaks. Duntov does this, and @GTR1999 has also recommended this to me, so I'm casually looking for an Eaton differential. https://www.duntovmotors.com/differentials-80-82.php
Save your nickels and dimes to add a third pedal to that car.
From '78-'81, the only automatic transmission the factory installed in Corvettes was the Turbo Hydra-Matic 350. It's a good, solid and reasonably tough transmission.
It should hold up as long as you still run the stock '81 190hp 350 in the car, and you're not getting serious about running it long and hard. Make sure the fluid and filter are clean.
From '68-'77, the factory mated the Turbo Hydra-Matic 400 (also a 3-speed) to high performance big and small block engines. That transmission was a more rugged, heavy-duty automatic that could withstand more punishment.
That vintage of THM-350 was not designed to handle copious amounts of torque. It would probably do well up to 150% of the engine torque available from factory engines (which were paired with the THM-350). You can have your transmission rebuilt with stronger parts, if needed; or you could exchange it for a sturdier unit...or a well-built overdrive automatic.
Is the 3 speed automatic in the C3 1981 Vette good or bad? Can it handle begginer level HPDE?
3 speed auto is just fine.
If you put a good transmission cooler on it , shift kit, and service it ...........its good for 375 hp
Rear diff is fine too...... unless you intend to put slicks on the car and drag race.... the stock driveline is fine