Best ratio of armor vs insulation

Short Answer (Armor+Cold): Use Flak/Riot (for armor) and swap out Legs,Torso,Head,Hands/Feet for Fur as necessary if you need more cold protection (in that order)

Short Answer (Armor+Heat): Use Flak/Riot (for armor) and swap out Legs/Torso,Feet,Hands,Head for Ghillie as necessary if you need more Heat protection (in that order)

Note that this was tested in Version 236 without mods, and maybe be incorrect in the future. Also, I am only looking at primitive (engram quality) items, and you may very well have better results with higher quality pieces. I have included some tables at the end with the values of each item.

Lets look at the best overall armor in each category

For Hypo (Cold) Protection:
Fur(249) >> Hide(85) > Flak/Riot(60) > Chitin(40)

For Hyper (Heat) Protection:
Ghillie(70) > Cloth(60) > Naked(0) > Riot(-16.8) > Flak/Chitin/Hide(-25)
*Note that for Hands and Head, Cloth(15) > Ghillie(10)
Best total = 80 (All ghillie except cloth hands + head)

For good Armor:
Riot(575) > Flak(500) > Chitin(250) > Fur(200) > Ghillie (170)
*Note that top 3 order holds for hypo and hyper as well, with the exception of Chitin Hyper > Flak Hyper (slightly) for Legs and Chest

Both Fur and Ghillie Armor come out at the top of one type of insulation, and as they give respectable total armor they will often be the best choice for extreme weather, even if you expect to fight.

There is a trick for combining sets for armor and insulation. Except for ghillie, every piece will provide identical armor, but may not have identical insulation. Legs and Torso usually have stronger insulation effects (including negative ones).

For Armor and Hypo lets try combining Riot and Fur Gear. We are going to make one suit with Fur Torso/Legs/Head and Riot Hands/Feet. This provides 64+65+52+10+10 = 201 Hypothermic insulation, and 40+40+40+115+115 = 350 Armor. This gives identical armor and 51 more Hypothermic insulation than using Fur Riot Torso/Legs and Fur Head/Hands/Feet. It also gives 150 more armor than full Fur, at the cost of only 48 insulation. Note that using Flak instead of Riot only changes the total armor from 350 to 320.

Basically you can only really improve Hypothermic insulation of a Flak suit by substituting Legs,Torso,Head,Feet/Hands for Fur (preference in descending order). Without higher quality Hide, switching to Hide pieces is not a very good trade as it only increases protection by 5, at the cost of 80 armor.

These tables show the values I found for each armor piece.