Checking the rules for the petrified condition, Enlarge Person and for transmutation spells in general shows that there is nothing that mutually excludes both effects at once. Specifically, a petrified humanoid does not change type and become an "object" - it is still the creature, but with a condition applied.
There is no apparent "freezing" of ongoing effects, spell durations etc, which should really be noted under the condition if that was the case. There may even be undesirable exploits to make cheap permanent effects tied to petrified creatures under otherwise temporary effects.
So in my opinion, that supports your option 2:
(2) The petrification creates a statue of one's current form, but when
the spell wears off the new stone statue changes shape.
However, I think there is ample room for DM interpretation supporting either of the other two options, and even variations depending on what kind of effects can be "frozen in" when a character is petrified. It would be a minor ruling either way, and only require a little consistency during the game.
A side-effect of supporting option 2, is that if you cast any visible effect that does not affect normal objects on apparent statues, then you will see which ones are in fact petrified creatures from how the spell works (or not). As there is no competing "detect petrification" spell as far as I know, I think that is probably ok.
It's not stated explicitly, but limestone or marble seems the best fit
I'm not aware of any material that explicitly answers this, but the material components for the flesh to stone spell are "lime, water, and earth."
"Lime" is calcium oxide or calcium hydroxide, typically manufactured from limestone and mixed with water and sand/gravel to make concrete. Already limestone seems like an obvious fit.
Statues are commonly made out of marble… and that happens to be a metamorphosed form of limestone. This is also a strong contender.
Limestones and marbles are based primarily on calcium. As well as being present in the material components, it's also found in the human body in large quantities (in bones, in teeth, and as an important electrolyte). Humans are about 1.5% calcium by mass.
On the other hand, most other rocks involve significant quantities of silicon, but that's only a trace element in the human body (<0.1% by mass), and silicon isn't listed in the material components. ("Earth" could be just about anything from gravel to mulch; some would contain silicon, others wouldn't.)
So, going by both the material components and the human body, we're probably looking at a calcium-based rock without large amounts of silicon, which implies limestone or marble. It could even be concrete—it's a rock, though not a very romantic one.
I'm told (h/t Molot) that "In one of the Underworld books (prose, not rules) drows turned victims into onyx". While true onyx is a silicate, most "agate" sold today is in fact calcite (calcium carbonate), commonly found within limestone, so this is still consistent with the "calcium-based rock" interpretation.
If you want to enforce conservation of mass, then this fine answer's suggestion of pumice is definitely the best option, but spells are generally not known for respecting conservation of mass. For example, Iron Body multiplies a person's weight by ten.
Best Answer
That's an interesting idea. I wish I could find more corroboration for this, but it looks like it can be used for negative (and possibly horrifying) effect:
Looking at Petrified condition description:
(All emphasis here and below are mine)
So, at the very least, you could maim or cripple someone with this procedure, e.g. deforming or removing his limbs, damaging his face to ruin his appearance or senses, or leaving gashes and holes in his flesh.
Moreover, note the difference in description of Stone to Flesh in PF versus 3.5E:
Pathfinder:
3.5 Edition:
Maybe I'm reading too much into this, but note that between editions, an ordinary statue now becomes "a mass of inert flesh in the shape of the statue" rather than "a corpse". This suggests that any mass of stone added to the petrified character is something the spell 'doesn't know how to handle' - it won't create a complete and whole anatomy out of it (as in a corpse), but merely a mass of generic flesh.
So if you added stone wings to a petrified human, you won't end up with a winged human, but rather with a human with a pair of inert, fleshy growths generally shaped like wings - he won't be able to move them, and they'll just encumber him (and probably look quite grotesque, too).
I can't find much in the RAW to support this, and couldn't find anything to suggest you may gain a permanent benefit from this procedure. It obviously boils down to how your DM sees it.
However, it wouldn't make sense that this chain of effects will be a cheaper, stronger alternative to the effects of Permanency, which, for example, requires 2,500gp to permanently enlarge a target. Similarly, I couldn't find any permanent polymorph effect weaker than the 8th level spell Polymorph Any Object, so adding wings, limbs or other beneficial changes using the flesh-to-stone-to-flesh procedure seems really unbalanced.