What kind of portraits? Studio, street, casual on the spot, night, family, pets?..Lighting conditions? Would you consider a used outfit? What's your budget?
A D3000 or D5000 series camera probably isn't going to get you where you want to be. They're capable and take great photos, but controls can be lacking, (in my opinion, I have a D5500 I gave to my wife simply because I hated the controls) and they won't auto focus the older, yet still fantastic screw drive lenses.
The D3S and D700 are of the best build quality cameras Nikon ever made, they're both work horses capable of enduring hard use year after year, they're both old school and only available used though. D3S price ranges from $900-$1,200 U.S.D. D700 from $450-$550 U.S.D bodies only typically with a 180 day warrenty. I have two D700's and love them. Now the D750 is one of Nikon's best all around cameras, fully capable of what ever it's job is on any particular day or night. I bought a used D750 a few months ago and find it extremely capable and flexable under any light conditions. A used D750 will be between $850-1,200 U.S.D and well worth it.
The 24-120 f4 VR G ED AF-S is the ''kit'' lens typically supplied with a D750, I had one before I had a D750 and will say it's become a favorite of mine for it's image quality, size, and flexability, but there's better choices for portraits. I also have a 80-200 f2.8 AF-D ED I would choose as a better choice at the same price as the kit lens, (used). There are other choices, the 80-200 above is just mine in a zoom lens. In the long run, pay once-cry once.
A nice advantage with the D700 is the MB-D10 battery grip can easily be converted to take the large ENEL-4 battery giving you an all day power supply if that's a consideration. I've converted both of mine and life is good!