I’m looking into what shirt to wear under a PC, I want something that will keep me as cool as possible during the summer months. I have looked into 5.11 rapid half zip and their assault shirt. What should I look for? And what is popular and cost effective? I’m not worried about no melt and no drip, I won’t be in any combat zones

Cotton tshirt.

I wear a IIIa vest everyday and in my experience only under armor shirts have collars that won’t stretch out.  I don’t know if a plate carrier will pull on the collar like a concealable vest does but they are good to go in my book.

I wear a British under body armour combat shirt That's a t shirt or a combat shirt. When it's really hot I wear a custom combat shirt made out of litelok for the sleves and a UBACS for the body. For soft armor I wear the thinnest under armor knockoff I can get at academy.

And wash it, then soak it in a solution of water and baking soda. Then air dry it.
This will help assure that you don't get stinky under the shirt.
Seriously, it'll cut down on BO about 87%.

in hot climate cotton t should be fine. in climate that may get cold i would go with merino wool. not super durable but the wetness won't make you cold or stinky. you could use synthetics for either but you will stink.

I wear body armor every day and have been doing so almost every day for the last sixteen years.  I recommend a 50/50 cotton synthetic blend t shirt, which seems to offer a good balance of breathability, durability, comfort, odor reduction, etc, and most importantly, a reduction in the torturous phenomenon known as prickly heat (in my experience). Application and context are important here too.  Training? Professional use? Weather? Environment?  Depends, but, generally, my recommendation is a cheap/standard 50/50 cotton/synthetic blend.  If you want something more high speed than that, check out the Velocity Systems Boss Rugby or combat shirts from Crye, Patagonia, etc.

I m ASSUming from your question that you don't have any uniform requirements and this isn't for work, but general range use.  Armor sucks, even more so in the summer   You don't need a combat shirt for your needs( unless you want one for a specified "look"). A t shirt works, I prefer synthetics

No uniform requirements at all, definitely taking your advice on synthetics

Wise choice - I wear just a T w/ armor any chance I can-

If you need camo, look for Crye/Drifire combat shirts. If you look hard they can be found for a good price. If not, the Velocity Systems Boss Rugby shirts are a good bet.

I use a  British combat shirt for a combat shirt with a multicam type camo. The US Army style I own with Tshirt body is incredibly cheap and cheesy. The UK combat shirts are not that cool though but if you roll the sleeves and open the chest zip they are OK. The UK shirts are incredibly well made for ther price which can be had for so cheap its ridiculous to not own at least one (under 30 bucks). Im talking specifically about the green body MTP camo under body armor shirt. Its even Permethrin treated.

I have been temped to try the Ronin Alpha T in OD Green for pure summer use.  A cotton/poly Tshirt with multicam combat shirt pockets/velcro on the sleeves. Only negative is no collar to prevent sling chafe on neck. No clue on durability since I have not owned it.

As a Detective I wear an Elbeco UFX polo which is the finest tactical polo of its type and is cool with my plate carrier for all day wear, but being all poly it does not take well to sharp snags or male Velcro. If I wanted a red one for use as a firearms instructor or use for CID in black or navy its a no brainer top choice. For a green or tan for use with body armor in a class, yes with a caveat... its got a collar and is cool, also durable... just dont wash it with anything with velcro like combat shirt/pants, many 5.11 style tactical pants, etc. It cost almost $50 a shirt but lasts about 100 to 200 washes/wears then looks like it is worn with small straight snags and some pilling, but is still serviceable twice as long and looks new till then. You might get twice that if you keep it away from metal zippers as well as velcro.  Be aware it has some light stretch and shows your body flaws more than cotton if you are not in shape.

If we are talking soft body armor, I wear Underarmor heat gear. It lasts 100-200 wash/wears then looks like crap and the neck gets sloppy and hangs, its snagged, pilled, and looks like hell. I buy one or two per year and its DONE by years end worn on patrol. The new Underarmor is just crap compared to older stuff from 10 or 20 years ago when there was nylon in it. Its just disposable now IMO. I have 20 year old nylon UnderArmor boxer briefs that have 1000+ wash/wears that are excellent, almost like new with no snags or crazy pilling and even retained stretch, but nothing like them exists today. Everything is cheap 100% poly fabric from China now.

Just one man's opinion, but you're drastically overthinking this.

I have plenty of the nice, fancy uniform items, too, but if I'm not in need of camouflage and/or something in uniform, I usually wear an undershirt and a button-down. I do prefer long sleeves most of the time, even in the summer, better protection from sunburns, ricochets, hitting the dirt, etc., and you can always roll the sleeves up if you get too hot.

~Augee