KiwiStoker
If you don't need the pockets just buy some quick dry t-shirts or similar to ride in. Cotton soaks up the sweat and damp patches show.
I would just like to pipe in that cotton is a bad choice because it does not wick the dampness away from your skin and many a cyclist has ended up getting pretty sick from that myself included.

Otherwise there have been many good suggestions given I never regretted spending a few bucks on my first pair of cycling shorts or my first jersey, still wear them *gulp* 12 or 13 years later! Great investment!

Happy riding GenB and welcome!