There isn’t really a single “root” key. You choose the enharmonic names you want to use for the “black notes” (e.g. C# Eb F# G# Bb) and that defines how far you can go round the circle of fifths before you hit the wolf fifth.
With the choice of notes above (which was the most common version) meantone tuning then works out exactly the same for major scales of Bb, F, C, G, D, and A. In other words those major scales are “transposed” exactly. You can’t use E major because you don’t have D#, which is not the same pitch as Eb, and you can’t use Eb major because you don’t have Ab.
Many books make the inaccurate comment that “in unequal temperaments every key sounded different” but that is not true for meantone - there are only two different flavours of meantone, “good” and “unusable because of the wolf 5th”. It is true that for “well tempered” unequal temperaments where all keys are useable, every key does sound different.
For minor keys and transposed modes, the same general idea applies. In practice, the music only used key signatures of one sharp, and one or two flats, with occasional accidentals (e.g. F# and G# when the keynote is A).
If you choose to tune Ab instead of G#, you can then use the Eb scale (or C minor, or church modes transposed into C) but then you can’t use A (major, minor, or any other modes) because you don’t have G# for the leading note.
For the church modes, in practice the 6th and 7th degrees of the scale were used at two different pitches a semitone apart, similar to the modern melodic minor scale, so each “mode” actually included 9 pitches not 7. For example “D Dorian” used the notes D E F G A Bb B C C# D, not just D E F G A B C D. That mode “transposed” into G would then use G A Bb C D Eb E F F# G which still fits the notes in the meantone tuning. But you can’t transpose “D Dorian” into C, because you don’t have the note Ab.