Where is the complete list of all Army officer jobs?

Sir, thank you so much for the detailed answer. So once you are branch qualified, can you choose any FA you'd like? Are they dependent on your original branch? What do you mean by "new" 2LT branches, are they different then the ones on the link you posted?

You need to request accessions into the functional area, most you submit a packet and the highest qualified officers are selected, other's they select you. For the most part they do not have original branch requirements, but I'd guess there are some exceptions to this, none that I personally know, as officer's are supposed to be generalists, not detail subject matter experts (NCO and Warrant realms)
The new 2LT branches are the Army's core branches, those are on the goarmy.com website link. Most of those are open to any new 2LT others considered the professional corps have unique entry requirements, lawyers, chaplains, doctors, all of which require an advanced degree before you can submit to commission in their branches. I enlisted finance, commissioned as an Engineer, became a project manager, then submitted for the 51C contracting functional area. I've been happy doing so, but I do miss doing the fun Army stuff that is rare in the acquisition corps (but about the same as finance was)

SPC Benjamin Norman - see DA PAM 600-3 and look for Career Field Designation Board. That is the process to get into a Functional Area such as FA59