A chest rig is an excellent idea. When I started I got the same recommendation and got a Pantac AK chest rig like this one but in coyote brown:
I still use it to this day. It fits 2x AK mags or 3x M4/M16 mags per pouch, the pouches are tall enough to fit Thompson and MP40 magazines, I'm pretty sure I could fit P90 mags in there. There's also two molle spots on each side. I normally use them for a radio pouch on one side and a utility pouch on the other to hold my canteen. The AK mag pouches are big enough to fit pretty much anything, flash lights, compass, energy bars, etc. Even in real capacity games where I'd carry 10x 30 rounds M4 magazines, it would only use 3 of the 4 pouches. You can also fit a lot of things in the "map" pouch section, that's basically the whole interior of the chest rig, so it holds a LOT. And with the padded harness it's super comfy.
Also, on a hot July day, you will MUCH better off with a chest rig than a vest.