Watch the Greeny online guitar lesson by Jeff McErlain from Essentials: Chord Tone Soloing
If you want to outline the three chords as the soloist, it'll take some work, but hey, that's why you're here, right? A great quick start method is to use an A major pentatonic scale on the A7 or I chord and an A minor pentatonic scale on the IV and V chords. Interestingly enough, we'll cover some of the changes, which sound a lot like what Eric Clapton might do on "Crossroads". But, by doing that, we're still not thinking about our chord tones and strong notes, but it's a nice start.
I highly suggest writing out the notes of each chord on a piece of paper like this: A7 = AC#EG, D7 = DF#AC, E7 = EG#BD. Also, try writing out your scale options like this: Amin pent. = ACDEG, A Maj pent. = ABC#DEF#. When you see everything on paper, it can really clear up all the differences between the chords and scales. Trying to do this on the guitar or in your head can be really confusing. I do this to this day if I'm working on something new or if I'm presented with some difficult chord changes I'm not used to playing over. It really works!