Really almost any of the mirrorless systems will do what you want. I have a very nice 16x20 from an early Panasonic m4/3 camera, and it's cropped out of half the original image. Current offerings are capable of excellent image quality for prints.
I'd get one of the Fuji bodies, the excellent 14mm lens (21mm eq), and the 56mm f/1.2 lens for portraits. I'd probably toss in the 23mm f/2 as well for a solid 3-lens kit. If you get an XT1 used, they are going for a good price, even the X Pro 2 is very reasonable on the used market.
XT1, $700 used
14mm f/2.8 is $900 new, around $525 on eBay at the moment
23 f/2 is $450 new and a solid bargain (few used copies as it's so new)
56mm f/1.2 is $999 new, $750 or so on eBay
With some shopping around, I think you could stay in budget. You might also look at the 60mm macro which makes a nice portrait lens, or the new 50mm f/2, which is a great compact lens, but for me it's a little short for a primary portrait lens.
Image quality from the XT1 is good, though processing raw files from any Fuji X-Trans sensor is different from standard Bayer-pattern sensors. If I can figure it out, you can.
The camera handles well, with plenty of physical manual controls and a decent menu interface.