Of the choices offered, the bolt action, with its powerful primary camming action extraction is the most mechanically reliable.
HOWEVER,
NONE of them are any more reliable than the operator.
Kudos to those who are paying attention to which sub-forum we are in.
If I recall correctly, the bolt was the quickest, been a while though.
Bet is has been a while! Tests I recall from the 60s & 70s, for 5 aimed shots, the bolt was ALWAYS the slowest. Semi auto, 5 seconds, pump, 6, lever 7, bolt 8-10. Times approximate, varying slightly with individual shooters, some shoot the lever faster than the pump, but the over all pattern is consistent.
Run some tests yourself. Its not that hard, if you got friends. Use a .22LR, available in all action types, and ensuring recoil of different rounds will not be a factor. Plus, its still as cheap as you can find. Get a pump, lever, and bolt .22 (this may be where the friends come in), and simply run some tests.
With good ammo, and a gun in proper working order, everything is equally reliable, providing the shooter doesn't jam it. With cruddy, damaged or out of spec ammo, the bolt has a slight mechanical advantage, BUT, its not a huge one, and crap ammo can exceed the rifle's ability to use it, easily.
I've seen a guy jam a Win Model 70, ENTIRELY though his faulty bolt operation. Short shuck a pump, or lever, or simply work them at the wrong speed, and they jam, too. Even when the gun and the ammo is fine.
In realistic terms, the most reliable action type is the one in the hands of the shooter who knows what they are doing, and does it right.
The most "reliable" action in mechanical terms can, and will jam in the hands of a shooter who doesn't operate it correctly.