Evo,
I don't really know the FAA requirements, but I think you've got it at least basically right. But if I were you, I'd go for the first option.
Two reasons for this. The training that you'll need to get an FAA license will almost certainly require a Visa. That will restrict your choice of schools, because you'll have to use a school which is certified to issue Visas. It also adds to the paperwork.
The other reason is that I can think of very few benefits of the unrestricted license, so why bother.
Having said that, there is one restriction, although it is not really enforced - and that's if you want to do your night qualification in the US. The FARs allow you to add any rating to your foreign-based license. But since there's no such thing as a FAR night rating, you can't add that to your license, so it's not possible to solo at night on your foreign-based license unless you already hold a UK night qualification. The solution is to issue you a student license (for solo flight only) or an unrestricted FAA PPL (if you want to take pax at night).
(The CFI at the school I flew from, who is also an experienced examiner, was unaware of this, and had been allowing UK students to solo at night, after receiving the more stringent of the FAR/UK training requirements, for many years until I pointed it out to him. He then asked the FAA, who said that techinically, what I've said is correct, even though it's rather stupid. They keep meaning to change it, but since so many schools ignore the rule anyway there doesn't seem to be any real reason to bother changing it.)
FFF
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