If you play a ii-V-I in C major, all chords are taken from the key of C major, so in principle you can just play the C major scale over all three chords. Over the Dm7 chord this would be a D dorian scale, and over G7 it is a G mixolydian scale. But note that D dorian, G mixolydian, and C major all share the same notes; they're basically just the C major scale started on different roots.
Apart from chromatic passing and approach notes, which are always possible, you can add extra notes when playing over the V chord (G7). In jazz, it is common to add alterations to the V chord:
#9 Bb (actually A#)
You don't need to add all of them. You can try starting with the b9, which means that you'd still play G mixolydian over G7, but you exchange the note A for an Ab, which is usually resolved to the note G over Cmaj7.
A scale that has all altered notes is the G altered scale (7th mode of Ab melodic minor):
G Ab Bb B C# Eb F
So if you like you can switch from D dorian over Dm7 to G altered over G7 and back to C major over Cmaj7.
There are many other possible scales that can be played over G7 (e.g., whole tone, half-whole, phrygian dominant), but note that the way you resolve tension is at least as import as the exact notes that you choose over the V chord. As long as you resolve nicely, anything goes.
If you're not yet familiar with playing over a ii-V-I progression, I'd suggest that you mainly stick to the C major scale, concentrating on emphasizing chord tones over each of the three chords. Later on you can be more adventurous and use alterations and the scales I suggested above.
Concerning the second part of your question, I don't see how the circle of fifths will help you with improvising over a ii-V-I progression.