All of the chords in both the verse and the chords are in the key of E Major (E Ionian). You will be happy to know that this makes soloing a relative breeze as you can play one scale and as the chords change, the mood of the notes change with it. I am not sure how you are with your theory but you can think of Me and My Uncle. The chords in the first few lines of the verse are E minor to G. Jerry can run on the E minor pentatonic scale which has the same notes as the G major pentatonic scale and as the chords change underneath his runs, the mood goes from happy to dark. Much the same for Dark Star and the A Mixolydian scale which is the same as E dorian, a relative minor of A Mixo. "Dark Star crashes...". The ethereal mood for the first two lines of the song are the sound of A mixolydian. When the lyric goes to "Searchlight casting.." the mood takes a definite shift towards the dark and evil which is really just Phil changing the root note from A to E. Jerry can still play the same notes but now they have a totally different mood.
For your tune the key is E major more specifically, E Ionian so your choices for soloing in that key are E Ionian and all the relative scales in that key such as F# Dorian and so on. If you aren't cool with the 7 tone scales, you can use pentatonics. The one that will work the best is A major pentatonic which is the same as F# minor pentatonic. The tones you are looking for are all there for every chord in your tune. You might want to think of it in terms of F# minor pentatonic as that is where your verse lines begin and end. Here is a decent link for some scales in case you aren't familiar with them. Good luck.