One thing about the Graflex press cameras, is that if you are doing portraits in what I assume will be in 'portrait mode' (vertical orientation), you will always be using the camera turned 90 degrees. My older Speed Graphic does have a tripod mount hole on the side as well as the bottom.
But something with a rotating or reversable back might be nice. (The more expensive Super Graphics have one, I believe). But even wood folders can be carried around on the tripod. Many of the lightweight wood folders like the Tachihara, Horseman Woodman, etc, weigh under 4 pounds. An alternative to consider. I have a Calumet PocketView, which is a lightweight rail 4x5. With the Caltar IIN 150mm on the it, the camera weighs 2.5 pounds. Some people's tripod heads weigh more than that! So there are several alternatives.
A 210mm lens might be nicer for head-and-shoulder portraits, but if you like the look of your MF portraits with an 80mm lens, then the 150mm with the 4x5 will suit you fine. I don't think you'll find a 210mm that will fold into the camera. The Caltar IIN 150mm/5.6 lens is sweet and usually inexpensive (it is actually a high quality Rodenstock). The Copal 0 shutter is small and dependable. It is a good all-purpose lens. You can easily work with older lenses, some even have a softer look to the images that can well suit portraits, but one must deal with some less-than-perfect shutters.
You camera, whatever you decide to get, will have lensboards that fit on to it. These lensboards often fit only one brand of camera, but there are exceptions. These boards are drilled with holes sized to fit a particular lens or shutter. For example, you might have a board with a hole sized to fit the Copal 0 shutter...all lenses mounted in Copal 0 shutters will fit on that lensboard. The lenses usually require a retaining ring or jam nut on the back to attach it to the lens board, so make sure a lens you buy comes with one.