And yes, I have studied the theory and I know the three "coincidences" in major scales.
My teacher had me start with C#, then F#, then B, and then the group C, G, D, A, E which have the same fingering, but in reverse (from E to C). He maintains that starting from C major is not advisable because it is more "tricky" than the others since it has no black keys.
And he is perfectly right.
While waiting to resume lessons, I am moving on to the group F, Bb, Eb, and Ab. However, I do not know the fingerings, so I asked for enlightenment.
Then one moves on to the minor scales (natural, melodic, and harmonic).
It will take me quite a while.
But, piano study and "hurrying to do everything" don't seem to go well together.
Scales are grouped into fingering "families" and every day one must keep one for each family at hand. F major, like B flat major, is part of those "exceptional" ones for which - in general - a different approach to the subject is better.