The window of time between when you activate a grounded shinespark and when you can press a directional button is half a second -- specifically, if you press jump to activate it on Frame 0, you can press right and jump as early as Frame 2, and as late as Frame 30. Jump technically doesn't need to be held, but that will be easiest for all non-TAS runs. If the inputs aren't correctly done for an angle or horizontal shinespark in this window, it will be vertical.

The window of time to press right or angle up with an aerial shinespark is almost the same as a grounded shinespark -- 1 to 29 frames after activating it, instead of 2 to 30.

This video shows the shinespark being activated on the last frame possible (3 seconds after charging), and then the shinespark being started on the last frame (half a second after activating).