Finding Out Which Mode To Use Options

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I have a question about how to find the correct mode.

Lets say we compose a jazzy II - V - I progression, for example in C major.
Then we would get the chords dm7 - G7 - Cmaj7.

And now we want to make a solo over this backing, how do we find out the correct mode to use over which chord?
My guess now is that over the dm7 chord, we have a flat 7th and should therefore use a mode with that; the mixolydian mode. And since the mixolydian scale is the 4th mode in C major, we go 4 steps from the C and finds F. So over our dm7 chord we use F mixolydian scale.

Or now I'm getting confused, since the G7 also has a flat 7th, aare we going to use the F mixolydian again and then go for C Ionian over the Cmaj7?

Please help me understand this mess
Thanks!

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