I got a lot out of Matt’s monthly lessons on modes. As far as a goto place to start playing notes along with something my favorite is mixolydian. It is very useful to have the root right in the middle there.
C to A string for the key of F.
0 1 3
0 1 3
If you learn all the notes on the E string, you have a great place to start for any key. Also works well with the dominant 7th chord, but put that to the side if not sure what that means.
I then like extending that into other modes for the key you are in including an extended pentatonic.
This “extended pentatonic” is seen in the guitar “fretboard logic” books and the pattern can be used for major or minor of course depending on which note you are starting/referencing.
Here is an example for the key of G or Em, string G to A.
0 2 4
3 5 7
7 9 11
10 12 14
You can check where the G is and the E for minor pentatonic and use same “pattern” for any key.