Building code and safety for kids both dictate that your railing and stair balusters be no more than four inches apart. Aesthetics dictate that they be spaced evenly. There are a ton of different methods for achieving this goal. This was mine:
Handrail Builder. It cost $1.99, but saved me many hours of head scratching. Put in the span you're looking to cover and the width of your balusters, and the app will give you the spacing. Cut a spacer out of scrap materials, write the width on it (in case you need one of that size for a later stretch of railing), and cut a handle in the middle so you can hold the spacer and ad the baluster with one hand while you drive screws with the other.
I also suggest starting from either side of the railing, then working toward the middle. If you're off even a little in cutting your spacer block, the error will compound until it's definitely noticeable. You can correct that by playing around with the spacing of the last couple of balusters, and it's a lot harder to see the results of your tweaking if it's in the middle of a run, rather than all at one end.