I've posted about Owl Hoot Trail before and have lauded it's rules simplicity. So I whipped up a quick hack for playing Post Apocalypse stuff. If you want to start now, just roll on the GW mutation table of your choice and adapt; it's pretty easy. The easiest choice would be Mutant Future, using their weapons and tech items as well and just porting in the OHT system.
To change some terms, GUTS corresponds with GRIT, SPEED with DRAW and BRAINS with WITS. Mutations would work in that for every two beneficial mutations, you'd have to take a drawback.
Here's how radiation would work:
If exposed to radiation, you must make a GUTS + Toughness roll against a DC of 15 for background levels of radiation, 20 for moderate levels, 25 for high levels and 30 for ground zero levels. The frequency rolled is determined how close you are to the source. If you fail, you take 1d4 damage to GUTS (recovers 1 point a day). Every time you lose 1/4th of your GUTS score, roll 1d6. On a 1-4, you gain a mutation drawback. On a 5 or 6, you get a mutation benefit.
Identifying tech items would be a BRAINS + Learning against the DC you think works.
Origin - Waster (same as native), Sheltered (same as greenhorn)
Humans, +1 to all skills, extra creds
Mutant - +1 Guts, +1 Toughness. Free mutation sans drawback
Animal - +1 to choice, +1 Wilderness. 1d6 natural weapon
Plant - +1 speed, +1 Amity. Hardy 1
Constuct - +1 Brains, +1 Learning. Move 3/4 as fast everyone else. Can't eat,
drink or be poisoned/sick. +3 to fix objects
Soldiers are experienced in all kinds of combat. They have a +3 to Toughness.
If a Soldier has a GUTS of +1 or more, they get a +1 to hit and damage with
any weapon they hold. This bonus increases by +1 at 3rd level and every 3
levels after. A soldier with a SPEED of +1 or more can make an additional
attack against an adjacent enemy (or one within range for shooting) if he kills
his original target. This can only be done once (no stacking cleaves)
Scavengers roam the ruins of the wastelands looking for junk to sell or artifacts to steal.
They get a +1 to Toughness and a +2 to Wile. If they have a SPEED score of +1,
Scavengers get a +1 bonus to disarm traps, unlock doors and avoid detection. This
bonus increase by +1 at 3rd level and every 3 levels after. If a Scavenger has
a Brains score of +1, they can re-roll one technology roll every day
Scouts are the watchmen and pathfinders of what remains of the world. They get a +3 to Wilderness.
If they have a SPEED score of +1, they move about 1.5 times as fast as everyone else and they do
not go last in initative if they are moving (though they still suffer the defense decrease).
A third level Scout with a GUTS score of +1 may find themselves a mutant creature to train as
a companion. This companion increases with level like the Scout.
Medics are shamans, doctors and medicine men of the wastes. They get a +1 to Amity and +2 to
Learning. If they have a BRAINS score of +1, they can provide a character with 1d6 temporary hit points per day.
They can do this an additional time at level 3 and every 3 levels after. If they have
a GUTS score of +1, they add a +3 bonus to help heal injuries.
Psykers are mutants who have harnessed their mental abilities beyond that of normal mental
mutations. They have a +3 to Wile. If they have a BRAINS score of +1, they can "boost" a mental
mutation once per day, doubling it's effectiveness. They get an additional use at level 3 and every 3
levels after. A Psyker also starts with a free mental mutation that doesn't count towards drawbacks.
Chroniclers are leaders, storytellers and bards of the wastelands. They have a +1 to Learning and a +2
to Amity. If they have a GUTS score of +1, they can give themselves on an ally a re-roll on any
roll once per day, though they must take the second result. This increases to two uses at level 3 and
an additional use every 3 levels after. If they have a BRAINS of +1, they can roll a BRAINS + Learning
test against a DC of 15 to see if they know anything about an area, creature or artifact regardless
of if they have encountered it before.