Default [Q] Expected Stock FW? Also, Custom ROM Note 2 vs Note 3 Root?

I'm trying to decide whether to get a Note 2 or a Note 3 (AT&T), and I am having issues finding answers to valuable questions that should help me decide.

First of all, I believe that my options will end up being:
  • Get a Note 2, be able to root and install custom ROMs to my heart's content. Basically unlimited possibilities here, at the cost of less performance.
  • Get a Note 3, possibly be able to root (this is important), not able to install custom ROMs ever or until a way around the locked bootloader is found.

Assuming I'm correct, my real questions are as follows:
  1. What's the expectation with regards to being able to root an AT&T Galaxy Note 3 fresh out of the box? Basically, if I order a Note 3 from Amazon today, should I expect it to be unrootable? Should it more than likely be rootable as long as I don't OTA update? Does anyone have experience buying a Note 3 very recently, and has any info about what their out-of-the-box firmware was? Where did you buy it from, would I have better luck getting one from best buy?
  2. Does anyone know the type of performance expectations I should have between the Note 2 (with whatever custom ROM suits your fancy) and a rooted Note 3 (preferably with all non-essential apps frozen, what I would expect to be a similar experience to a lean custom ROM on a note 2.)

I'd be interested in any performance comparisons, especially "how it feels" types of generalizations, because while I can look at anandtech articles all day and see how they stack up in benchmarks together, they don't take into account lean custom ROMs or rooting, and I'm looking for everyday use types of things. I want to be able to know that whatever random app or game I play won't be artificially limited in performance by having unnecessary background apps running, so rooting/freezing is important.

For example, I'm planning to get a smart dock and use a mouse and keyboard, hooked up to a 1080p monitor and run basically whatever I feel like running such as splashtop streamer, but have no idea what types of performance differences I could expect, not to mention how exactly hooking up to a monitor works with either phone. Does the note 2 output at a lower resolution than the note 3, therefore the note 3 would be outputting full 1080p? Can you output in whatever resolution/orientation you want?