I don't think there's a "right" answer to your question. Different players will have different methods.

I tend to learn the rhythm guitar first, or at least what chords are used where. Then the lead guitar parts. Solos are usually the hardest to get up to speed.

You'll probably find some parts are easier than others.

Really, it's all down to what works best for you, but I'd recommend learning the rhythm guitar parts first for all sections. Then lead guitar for all but save solos until last.

I never worry about getting up to speed until I've memorized everything, but then find I have to spend some time just working on the trickier parts repeatedly instead of playing the whole song.