For me this is not about how you want your structure and not trying to change a structure to meet your analytics needs. Analytics can be set to handle any structure you choose, even if it can take some tweeking of the installation of the script, but In my experience, you allways have to do a custom installation of Analytics to get what you want anyhow.
So the question should rather be, should you have category paths in your urls or not and that is a much tougher questions.
First, we need to understand that the shorter URLs you can have, but still have good "readability" for the user, the better it is, but you still want to have a good structure for inbound linking.
I think, to make this fairly complex issue more simple I would say, that if you run content at your category pages, with the possibility to shop products and display of campaign information, then you really need to have the category in your URL.
This is because you want the user to be able to just delete the product in the url after finding it in Google to get to the category of that product. For inbound linking its also nice to have a clear and nice category in the URL.
On the other hand, if you dont have content on your category pages, then I woulnd't display them in the URL, mostly for the same, but oppositie, reason as above and as you get shorter URLs
You should not add parameters to your URLs if you dont need them.
If you still go ahead with parameters, just make sure you add link-cannonical to point on the none parameter url, to prevent duplicate urls of the same products