For the Axe, honestly either unit will be fine. It’s important to understand that they sound exactly the same, it’s just that the mkII has a little extra trunk space and a cup holder. For rocking out with a great classic tone, or thrashing out some metal, you won’t notice any difference. Remember it’s for making music - we tend to get distracted by chip specs and forget that sometimes.
As for headphones or monitoring, be mindful that the axe will only sound as good as the speaker it’s going through. If you get cheaper phones, don’t be disheartened if it sounds bad at first- it’s not the axe! I was very disappointed at first because I was using poor quality monitors at low volume and it sounded like plop. Now I use Presonus Eris monitors - not expensive but “good enough”, and I TURN IT UP! 90db minimum. I also use Shure SE215 IEMs live, which are cheap and sound fine. There’s another option.
Personally I would go the mkII turbo just because, since it’s easier to upgrade your monitoring later than it is to upgrade the axe. But if you don’t think you’ll be able to save for better headphones later, the MkI is still a Ferrari and you will be perfectly happy with it. For example, I would have absolutely no use for the extra space in a mkII since I only use one preset, and I never get anywhere near the CPU limit.