Is the shape of the cartridge a large contributing factor to the reliability of the AK or is it the gas system/loose tolerances/one moving part etc.? When I leave PRK, I'm going to get one and am trying to decide on caliber.

The cartridge taper gives the cartridge an instant release from the chamber.  A slight rearward movement, will give a total release.  This is important, but not as important as the giant mass of the AK carrier and the ample clearances given to all moving parts.  A properly designed 5.56 AK will be nearly as reliable as the Eastern calibers, only sacrificing that extra amount given by a tapered cartridge.

Your question is good, but it's the wrong question.  Part of the reliability built into the AK system is the magazine quality.  Any 5.56 AK will suffer unless using a mag designed originally for 5.56.  Many alter 5.45 mags for 5.56 use, which is not really a good idea.  If you buy a 5.56 AK, get Weiger mags.  These are available, and were originally built for a 5.56 AK, that was ultimately scrapped.  If you use an altered 5.45 mag, your mileage may vary.

In my opinion, 7.62*39 is an excellent caliber, and should be your first choice in an AK.

Ditto on the Weiger mags.I have a .223 Saiga that runs great with them.

Taper does NOT give "instant release".  In fact, it increases residual bolt thrust and unless the action allows for a taper in the locking mechanism, this will tend to INCREASE the bolt lift force.  Look at Weatherby cartridges.  Look at P.O. Ackley Improved cartridge.  Both design philosophies are parallel walled.  Why?  The .250 Ackley Improved was designed for the Savage 99 lever action and higher pressures in the regular .250-3000 would LOCK the bolt from residual bolt thrust.  What is residual bolt thrust?  At the moment of highest chamber pressure, the cartridge head pushes on the bolt with a force of the pressure multiplied by the largest diameter, usually the case head OD.  The bolt is now compressed and there is a slight elastic deformation of this assembly against tyhe locking surfaces.  With a tapered cartridge, the case head also EXPANDS along the tapered chamber, increasing the diameter.  When the pressure subsides, the bolt compression is relieved BUT the case is slightly larger.  Something has to give and the case goes into compression, binding it in the chamber.

In bolt guns, this is almost never a problem because the case cools and shrinks slightly but in an automatic, it is a definite problem IF the pressure is high.  This is why all high pressure cartridges are nearly straight walled.

I can only speak with experience on the 5.56 AK.  I had an under folder I bought in 1985. Damn I wish I still had it. Anyway, it would fire all day long without a jam. I got it so hot it melted the varnish from the handguard. It still worked just fine.  One drawback however. It put a very deep dent in the brass on ejecting it. The only way to reload the brass was to fire form it back to its original shape. It was too much of a pain in the ass. I have a 7.62X39 AK now and it's great.