I am not sure about your location. If you are in the far north it is a great policy to insulate your basement floors - rigid foam sheets and OSB is certainly a great way to do it and probably the easiest.
However if you are in a mixed climate, I am not sure what you are looking for out of the insulated floor. The energy savings will not be there as cool months will be offset by warmer months. Also with a well insulated finished basement, you shouldn't even feel a "cool" floor in the winter unless you are tiling. I live in a moderate climate. When it is 0 degrees Fahrenheit, my basement carpet is not cold.
So first think about why you are doing this. By having this "waterproof" barrier on your floor you are not fixing water issues, you are just making it longer before you notice them. If my basement sprung a leak I would want to know right away, not after a few weeks when I start noticing mold grow everywhere. Also note that you will have more work to do if you get a leak because now you have to move all of the subfloor from the area being worked on - and dry the subfloor. You may have to remove a lot of the subfloor to dry it out or get fans to it.
As far as the install I have done both methods - laying out the sublfloor (or dricore which I have used many times - bigger pain than the foam+plywood) first or framing then subfloor. It really doesn't matter which you do. Either way your drywall is well above where water should get to and that is the main organic material you are worried about. (you obviously don't install subfloor after drywalling)
Now my preference is framing everything first, even if I have to make more cuts to my sheeting. Framing on top of dricore or foam+plywood is a pain in the ass to put it mildly. The dricore teeters - note much of your framing will be along the outside walls and of course that means you will be framing on the edges of your dricore or sheets. The sheets teeter, but not as bad as the dricore, however they smoosh. Your cuts have to be super accurate, as if the wall is too tall even by a 1/16" it will push down board, which pushes up other end. Then your next section of wall is too short by 1/32" and it is sort of floating, while its plywood may pull up when nailed/screwed and the plywood next to it is smooshed so now there is a slight ridge (so we start shimming out the damn framing like cabinet). Don't even get me started on getting the wall at a perfect 90 degrees and not realizing you have pushed the plywood in a certain direction by a 1/4", you push that back and damn it your sections don't line up right. Don't get me wrong it isn't rocket science and you can frame on top, just takes longer and prepare for at least some mild frustration.