For Hellyer clinchers are fine. Used a mix of Vittoria Open Corsas, Ultraspeeds and Rubino Pros all without issue.
You want a tire with a decent TPI (threads per inch) count cause the casing is nice and supple and they can generally go to 125 PSI with ease.
I personally stay away from any coloured tires or with coloured stripes, they tend to be not as grippy.