When you get tired of wearing the same shirts to the gym, do not wear a light gray 100% cotton shirt instead. It will immediately show sweaty pits, sweaty neck, sweaty back, and when you get super sweaty, a sweaty belly button. This no light gray rule applies to all cotton knit shorts. Not pretty. If you are going to go all cotton, stick with dark colors. On top of that, my shirt had 3/4 sleeves.
Dri-fit and other wicking fabrics totally make a difference. Eventually, sweat marks will appear, but it is more gradual. You can get good deals at TJ Maxx or Target. I haven't tried any Old Navy stuff, but they do have a large selection these days. Time to go get a new shirt. Maybe this one.