Right, iterating through pixels is better. The tricky part about iterating the angle is that you need to choose the step size correctly or else you could skip pixels. Like if you iterate in 1-degree increments, you'll plot 360 pixels total, but the size of the circle on your canvas might be more than 360 pixels wide. I'm sure there's a way to choose the angle iteration step size to guarantee not skipping pixels, but you'd often duplicate work and re-plot the same pixel twice.

So yes, start at (R, 0), increment the y-coordinate each time and possibly decrement the x-coordinate, until x=y which will be at 45°. If the circle's center is an integer on the pixel grid, you can reflect/translate each pixel in that first octant to all eight as you go. If the center is fractionally positioned, you'd have to calculate it all the way around, iterating primarily on y or x depending on the location.