Respectfully, I am of the opinion that the armor classification (Light, Medium, Heavy) should first and foremost reflect on how heavy and relatively clumsy the armor is to move in, this way it would make the most sense.. That being said, a mere 35 Lbs of Metal Armor already counts as 'Heavy' and gives a -1 Agility penalty despite being only a partial coverage armor set with a flexible leather undersuit as a harness. Based on the lore from all of the games so far, I'd consider all types of Fallout powerarmors by their very definition as 'Heavy' armors. Exception from this rule should require a very good explanation/reasoning; What exactly makes the Tesla Powerarmor so much more faster, mobile, flexible and thinner than any other make of powerarmor? Why are there no other powerarmors in existence which would count as medium?
Note: Original Tesla Armor from Fallout 1 and 2 was basically a variant of the Metal Armor - Non-powered armor set offering extra protection versus energy attacks. This would suggest that the 'Tesla' in these tesla armors is very likely to be a rare modification or an upgrade to some metal surfaced armors. This reasoning would suggest that the NV tesla power armor would be functionally otherwise identical to the Remnants powerarmor except for its better energy protection. (Hypothetical NV tesla metal armor, which is not in the game, would also still count as heavy, because metal armors are all heavy by definition in game. Hypothetical NV Tesla Combat Armor would be Medium though.)
the 'Walking Tank' description text is propably mostly like overtly optimistic advertisement speak; 'Wearable Combat Robot' would be a more accurate description IMHO. Handheld weapons much less powerful than a missile launcher can be used to punch through Fallout powerarmors, even in Fallouts 1, 2 and NV which I would still consider as the primary lore sources (games written by the original devs)..
In F3 and F4, the walking tank term is even more strongly contrasted in gameplay by even the lightest of weapons being able to do damage through the armor - In F3 it was possible to kill Enclave powerarmor troopers with a BB gun or a knife, and in F4 it is easily possible to use a .38 pipe SMG (a cheapass gun built from random scrap, firing a fairly low power pistol round) to hose off all of the armor plates from a T-60 BOS powerarmor and thereafter killing the dumbfounded paladin wearing only the remaining skeletal powerharness. (The F3 and F4 issues stem from using the inferior 'Damage Resistance' armor gameplay mechanic, which makes all armor 'soft' with no exceptions - 'Damage Treshold' as used in F1, F2 and NV is much better.).
My opinion of Fallout powerarmor protection value order, based on lore first and gameplay second, would be like this;
Including FNV, F4, F3, F2, F1, from worst to best;
Raider, T-45, T-51, T-60, X-01, APA, Tesla PA, APA Mk II/Enclave PA, Hellfire.
And the same, without any F4 armors included, basically agreeing with darthbdaman's type 1 option;
T-45, T-51, APA/Remnants, Tesla PA, APA Mk II/Enclave PA, Hellfire.
(Note however, that Tesla and Hellfire IMO should not necessarily offer notably much better (just a bit better perhaps) generic protection than the previous tier overall, other than offering very specific extra protection versus energy (Tesla) and fire (Hellfire) damage types.)
