First off, what brand of invisible thread are you using? It should be as thin as a strand of hair. I used to use YLI .003 invisible thread with no problem; it is very, very fine. Nowadays I see that Sulky invisible thread is often recommended. I have some of that but haven't used it yet.
Aside from putting the spool in a jar or using a free-standing spool holder (and checking the spool for a nick is always good too!), you can tape a large, closed safety pin to the right back edge of your machine with the circle part up and run your thread through that before doing your usual threading. It helps keep the tension on that top thread smooth.
Because invisible thread has more stretch, you usually want to loosen your top tension.
Are you using the invisible thread in the bobbin also? Again, because this thread stretches, you have to be extra-careful when winding the bobbin so that the thread isn't being stretched. Wind slowly. Also, stop before the bobbin is completely full. It's easy to over-fill a bobbin with invisible thread.