I have to agree with tirediron..buy a used tripod and head. New tripods are very high-priced compared to used ones. I also second pendennis's idea: "When posing a subject you also have to allow for some framing movement. If you frame too tightly, you lose room for any errors. You may want to allow for a bit more room, and edit a bit tighter in your editing app."
As far as framing precisely: I like a ball head, and I just simply move the camera as needed with the ball set to a moderate tension level, then lock it down for shooting.
If you really want to know...I think shooting off of a monopod is easier for vertical portraits...fast,easy,and it allows you to maintain the right camera height. I see absolutely no need for a geared tripod head for portraits, even though I used to shoot high-volume studio portraiture using an electrically-operated geared head and a huge, 30-pound long-roll camera on a rolling camera stand. A geared head is fine for a huge, heavy camera, but unnecessary for most modern d-slrs and mirrorless cams.
On longer,half-body and ful-length portraits, an important aspect is the idea of keeping the camera back plano-parallel with the subject or "the back wall of the room"...too many people shoot from too high or too low, and angle the camera downward at their subjects.