If you are planning on screenprinting this design, the optimum size and resolution would be 180-220 dpi and actual print size that you would be printing on your shirt.
Most likely, your design will need to be vectorized, which, judging by your art, should be easy.
If you are printing a heat transfer or using a
DTG machine, actual print size at 300 dpi is best. CMYK mode for transfers, RGB for
DTG.
When using Photoshop to design t-shirts, you want to start out with a document size that is the same size that your print will be, and a resolution (dpi) that fits the type of printing you will be doing. It's probably a safe bet to always start out at 300 dpi, and then you can always scale down for screenprinting if needed.
If you start out at a resolution lower than what's needed for screenprinting, the end result will not be the best, but it can still be done.
Hope this helps...