It depends on more than thickness. From a historical perspective, armors were almost always of differential thickness because the plates were forged out from blooms into sheets, so real armors were thicker where they needed to be thick and thinner where they didn't. A breastplate for example may be thicker in the center and maybe out to the left side and thinner on the right side, or a helmet would be thicker in the visor and center of the skull and then thinner out to the edges. This is partially the way the plates were hammered out from blooms and that armors tended to be raised from one piece so you could 'push' metal into the parts that need it during the raising process. Modern steel is of course manufactured in perfectly uniform sheets so there's some compromise there. None of that really matters to your question, but I thought it would be good background information to have....
So, for modern armor, again, there's a lot more than thickness going on. Hardening comes into play a lot here. Mild steel (any steel with carbon content less than about 0.3%) cannot be heat hardened (it will get work hardened by beating it repeatedly with a hammer, but this is not the same thing, or as robust as heat hardening). This means when it's hit it dents relatively easily and if bent, it will remain bent. Medium and high carbon steels (>0.3% carbon) can be heated very hot and then quenched (rapidly cooled in oil, water or another solution), which re-aligns the structure of the steel in a way that makes it very hard, but brittle. So if you take hardened steel and drop it, it can crack or shatter. To make it usable as armor, you have to temper it. So it gets re-heated to a lower temperature than during hardening, and then is allowed to cool slowly. This alleviates some of the stresses created by the hardening process and leaves you with a steel that is hard, but not so hard that it is brittle. So it is very dent resistant, and when you bend it, it will spring back to the shape that it was formed into.
Modern steels in the US are often named by their carbon content, so 1050 steel is 0.5% carbon, 1045 is 0.45% carbon etc... Europe uses C50 or C45 as their naming convention. The reason I wrote all that is because a piece of 1050 carbon steel, hardened and tempered can give you similar performance in a lighter gauge than a mild steel in a heavier gauge.
Most people will tell you for helmets, you don't want anything lighter than 16 gauge, with 14 gauge being better. In addition to hardness, mass does help as well, since it will absorb impact if you're fighting in it. My helmet started life as 2mm steel and is now much thicker than that at the top and thinner than that at the edges because of the way it was made.
Other components don't need to be as thick. For example, the lames on my sabatons are probably like 20 or 22 gauge. But where it's going to keep you from getting brain damage, you want nice thick high quality steel. So I would suggest 14 or maybe 16 gauge for a helmet, and probably 18 for most other 'large' plates and getting lighter from there. Reputable armorers will know this and be able to guide you and make recommendations. You shouldn't have to tell the armorer every different gauge of steel to use on every component, but you should discuss the purpose of the armor (i.e. live steel fighting) so they know to use proper weights of steel.
At the $12k budget we talked about last night, that should be good enough to get you into something like 1050 spring steel, hardened and tempered. The great thing about hardened 1050 or other medium carbon steels, is that they don't dent nearly as easily as mild steel, so it's a little easier to maintain. Mild steel will need more heavy maintenance when it's getting beaten on frequently. So spring steels are a huge plus in the durability department.
Level of finish will affect maintenance as well. A nice satin finish will help prevent rust. But no armor is 'rust proof' unless it's stainless steel, but that's not a historical steel and is usually obnoxiously shiny so I don't recommend it. The smoother the polish, the more resistant to rust (less microscopic nooks and crannies for water to get into). Regardless of whether it's mild or medium C steel, you will need to keep it oiled, and remove light surface rust from time to time (just part of the game).
Historically armors were made from pure iron (0% carbon) to medium and even high carbon steels. In the 14th century hardening became more common, so using a hardened steel is still very historical. Interesting side note, they understood *how* to harden, but they didn't always seem to understand *why* certain steels could be hardened. We have evidence that some pure iron armors and low carbon steel armors were put through the heat treating process (which won't do anything).
TL:DR
If you are willing to spend upwards of 10-12K on a harness, go for a nice medium carbon hardened/tempered spring steel armor in appropriate thicknesses (probably at least 16 if not 14 gauge for your head).
