Instead of buying cheap cotton shirts in bulk, try buying a few good merino wool t-shirts from a responsible manufacturer, locally produced under much better labor conditions. It will also impact the environment less, partly because cotton production uses ridiculous amounts of water and partly because you're not having products shipped to you from halfway around the globe.
A merino wool t-shirt will be more comfortable, last longer and be more resistant to dirt and odors, as well as regulate temperature much better. For normal day-to-day use, you can alternate between two shirts. Hang the shirt in the bathroom while you shower, then air it out in your bedroom for 24h. You'll find that it doesn't hold on to odors, because the wool isn't absorbent like cotton. Give it a quick shake and wear it for another day, letting the other shirt air out.
Carry on-only travelers swear by merino wool because it's generally lighter than cotton and because you can wear it for several days or even a week like this. If you're not squeamish, you can even do this same routine with underwear, too.
People are so obsessed with quantity now, perhaps because it's an easily measured property. Try going for quality instead :-)
reminds me of this fascinating podcast about the history of textiles.
https://www.econtalk.org/virginia-postrel-on-textiles-and-th...
The fastest spinners in the world used to take 13 days 8hrs a day of labor to spin enough thread to make one pair of jeans. A 200 thread count bed sheet would take 59 days. And neither of those include the time turning that thread into fabric.
I'm still not going to wear obvious logos in general, and not wearing prints saves me from the most obvious stuff - and some things can't be avoided as easily. I'm not going to replace the backpacks I have: They were free and functional. I also sometimes have branded shoes because comfort is more important than a logo.