nice, thick "heavy body" or "high viscosity" acrylic paints (e.g. 'Golden' or 'Liquitex') work great on fabric (may eventually crack a bit if you put in a heated dryer after washing).
i've used them on cotton jersey (among other things) before, so t-shirts would be fine.
The white areas on the black T-shirt shirt will not be fabric - it will likely be Platisol, so any fabric paint will be a waste of time.
The white areas on the black T-shirt shirt will not be fabric - it will likely be Platisol, so any fabric paint will be a waste of time.