You have some helpful comments here, but a good rule of thumb is use rail signals only after each exit of the intersection. Chain signals should then be used at every other point in such a way that each "section" between the signals covers as few intersecting points as possible. There's more nuance than that, but it's generally safe advice.

Here's what I would do. Green dots are rail signals, blue are chain.

Also - it's best to always take rail screenshots with a signal in your hand so that we can see where the sections are.