I haven't carefully compared the wording of the various similar options (Wildshape, Polymorph, Shapechange and True Polymorph) so there might be some quirks I've been missing, but here's my general understanding:
1) First of all, "game statistics" are the stat block, conveniently made very visible in the Monster Manual layout. So the general idea of all these spells is that you completely toss aside your own character sheet, put the creature's stat block in front of you, and use that, including all its special actions (unless they require some equipment you don't have).
2) Your alignment and personality don't change. However it doesn't say if you're still aware of who you are or not. This seems really up to the DM, and it might be ruled differently also depending on the new form's Int score. (I think it's easier to rule that you are still aware, but the opposite can make for some interesting situations)
3) Speaking and handling objects might be impaired by the new form.
Think of 1) + 2) + 3) as your starting point, which is modified by the specific additions/restrictions mentioned by each spell.
- Polymorph & True Polymorph work similarly with each other (except the latter also allows objects), and the only additional rule to the starting point is:
x) Your equipment melds into the new form and becomes unusable.
- Wildshape & Shapechange work the same way (except duration, and number of form changes allowed), with the following exceptions to the general starting point:
a) Keep using your Int, Wis and Cha.
b) Keep your proficiency bonus to skills and ST.
c) Keep all your class/race/other features except spells and special senses (some other exceptions are possible depending on the form)
d) Choose if you want to keep/drop/merge with your equipment.
Note that it doesn't mention weapons/armors and tools proficiencies. But aren't these class/race/other features anyway? Personally I think it's safe to allow them.
Exception a) creates a slightly tricky case, when the monster has an Int/Wis/Cha proficiency that you don't have. You are supposed to use your own Int/Wis/Cha but also the monster's prof bonus, but you have to calculate it.
All in all I have only one reservation about this whole system... and that's about knowledge. There is no reason why you should gain or lose knowledge when changing form. If you know the barkeeper's name or how to enter Asmodeus' palace, why should you forget it while polymorphed? And if you didn't know it, why should you learn it by polymorphing? While this is obvious for free-form knowledge, the problem is that there are also knowledge skills, which by the RAW are affected. It may not happen often, but personally I will make an exception for knowledge skills and would not change what you know or don't know in case of polymorph.