I'd like to create a t-shirt with colour blotches on a plain black t-shirt, a bit similar to:
The t-shirt is cotton. Now my question is what type of colour to use. I'm considering synthetic resin varnish, do you think this would be durable enough?
Do you want the shirt to actually be wearable? If so, then "synthetic resin varnish" is entirely the wrong option.
For wearable clothing, you need a color that bonds with the fibers to endure wear and washing, but also remains soft to allow for comfortable wear. The best option for something like this would be a standard acrylic paint with a high opacity mixed with a fabric medium. The paint will provide the color, the opacity will allow it to stand out brightly against the black background, and the fabric medium mixed correctly helps the paint bond with the shirt's fibers instead of sitting on top. You could also use a dedicated (pre-mixed) fabric paint, which is often available in brighter opaque colors. Both these options are widely available at craft stores.
An additional option for adding designs to shirts is silkscreening ink, but fewer opaque pigments exist (bright colors on black are usually a double layer printing with an opaque white base). Because you're looking for bright colors in a splashed pattern, this is less likely to get the result you're looking for.