This answer is specifically about acoustic guitar sound board grading as as that's what your question refers to, there are other grading systems for other instrument building woods.
Different wood grades do not affect the tone.
Soundboards are graded on aesthetic properties: straightness of grain, grain spacing, angle of quartering, degree of figuring, imperfections, grain run out etc etc Theses criteria may have a positive or negative or no effect at all on the physical properties that determine 'tone'.
This grading criteria varies from wood to wood as different species are naturally different eg the tightness of grain on a AAA Sitka spruce will be different to the tightness of grain of a AAA Engelmann because these two species naturally have different tightness of grain, there is no consistent grading method across the board.
Tight, consistent grain may be graded high but it is often very plain looking and many prefer timber where the grain is more apparent and unique.
What is considered desirable in one top can be considered undesirable in others. eg poor grain spacing will be ignored if nice bear claw figuring is present (even though figuring has a negative effect on physical properties that affect tone! Like i said, grading is only about aesthetics).
Even if tops could be tested on 'tone' by some empirical means a grading system would still be useless. Good 'tone' for a classical guitar is totally different to good 'tone' for a Dreadnought. They have different goals and different tops will achieve those goals. An experienced luthier will know how to select the right top for their goal.
Of course, the construction quality is what matters most, a great piece of timber can make a terrible guitar by poor construction. The Taylor pallet guitars shows the reverse is true also.
In your average music shop the highest grade top will be AA, found on Gibsons, Martins Taylors etc You'll find many of these guitars are very fine indeed, and also some duds..
In conclusion, no ones first guitar is amazing, don't waste expensive wood on it. Your skill as a luthier will determine the quality of the guitar, not how many letters the seller attached to a piece of wood.