Photoshop has no random color create circle feature but you can randomize brush strokes via the brush settings panel and you can set the hue dynamics to the max as well as saturation to the max via the color dynamics entry.
Create a massive square bigger than the circle you want to use (create a selection and fill with gray etc and then define brush via the edit menu) or fill the entire document with gray or black etc and define based on that.
You have your stroke now and you need to select the paint tool to apply it (you should also have the tool recording ON in the actions panel right side menu).
Create a layer, this works best if it is on a new layer as the layer can then be re-positioned and re-sized etc and also duplicated. Create a circular selection using the ellipse marquee tool, this defines the size of the final preset.
Create an action for the rest of the work via the actions panel (window menu) and click the little + at the bottom of the panel or go to the right side menu and select new command.
You can find this command via the select menu and transform selection. Reduce the selection by 99% or 95% etc each time. Make certain that the center of the transform is the center of the document, you can do this via the view menu and new guide layout and 2 / 2 setting
The brush stroke should also be part of the action and as the color will change each time you apply it, the stroke will be applied to a smaller and smaller selection thus creating different colors in each of the selections. Stop the recording
Re-apply the action. You can do the same to create a square design or any design that has a transform of a selection (though not every shape is suitable for this).
You now have your design on a layer and you can now add effects to it or just simply duplicate the design and fill the entire image with your artwork (by holding down the alt / option and dragging). You can add effects via the layer menu or use the styles panel. You can also use the layer menu and smart object and convert and then add filters to this