Google plastic suppliers in your area. Unless you live in a town with a population of ten, there should be at least one, if not half a dozen. If you can't search it on their web site, you can call and ask. Sintra is a brand name that's come to be a common term for foamed PVC sheet. Like how Sheetrock has come to mean
any drywall, not just the stuff sold as that brand name.
Most people work with 3mm (1/8"). Some use 6mm, but that looks too chunky, usually, and is more grumpy about being asked to bend. I tend to use 1mm for my armor stuff, even though it's trickier to work (narrower window between "not hot enough to form" and "melting, curling mess" -- I've got a few failures in the wastebasket, I'm not ashamed to admit). Sintra only likes to take simple curves. To do compound curves, you may want to look at the same sorts of vents and darts you'd put into EVA. I do a laminar approach with my armor, either with additional strips of 1mm sintra at the edges to hold them in a specific shape, or some 1/8" sculpting armature wire glued in place and blended in. Gives the piece depth without making it a solid chunk. For example, my Jango boot armor, in progress:
And I
do use 3mm, too -- mainly for pieces that will stay flat or have only a simple curve.
Depending on the plastic supplier you find (also poke local sign shops to see if they use it, and if they have any they'd be willing to sell you -- or even large scraps that'd otherwise get thrown away), you may be able to get a quarter- or half-sheet, or they may only sell by the full 4'x8' sheet. Even then, that's under $50 for the 3mm from my supplier, and far less than that for the 1mm.
A last thought... Part of the reason EVA looks fake to me for armor like this is the thickness. My armor is mostly 16-gauge stainless steel (with the plastic stuff filling in until I get around to crafting or sourcing those components out of metal). Even with the rolled edges, there are still subtle cues to show the eye that it's not an eighth-inch thick all through. If one was toting around metal armor that thick, it'd weigh a
lot. Our brains are smarter than we think. We know that, even if not consciously, so when we see armor that looks like that, it strikes us as "wrong" in some way. Thick plates don't make someone look like a tank, they make them look like they're wearing fake armor. It might be brilliantly crafted, highly competent fake armor, but...

It works for Mass Effect because that armor is supposed to be some sort of lightweight composite, and never was meant to look like metal or ceramic plates. Then, at the other extreme, there are the space marines from Warhammer 40K. Thicker plates work for power armor, but they still have to be done right to not look like EVA.
--Jonah
[ETA: As for the amp in-helmet, that depends largely on your skill with electronics. Many people go with a headset with the wire fed down inside the neckseal to an amp/speaker in one of the pouches. The limited space inside the bucket makes a self-contained unit something that involves more work.]