All cameras today are excellent whether you shoot Canon, Sony, Nikon or Fuji. All the leading cameras now can produce very clean 14 bit (or more for medium format). This allows great potential for post production and editing. With a colour checker and custom profile you can really get the colours accurate or colour graded exactly how you want.
I know a number of portrait photographers who at the end of the session hand the jpegs out of camera to their client. With the right lighting, and knowing your camera you can get exactly the output you want. Many of these use Canon 1D and they love the out of camera jpegs.
Fuji is famous for their film simulations, if you liked one of their films then they have a simulation to match.
Hasselblad and Nikon tend to go for a more neutral look, I myself shoot a neutral flat profile with Nikon but have a number of Adobe Lightroom presets I have created to add the colour grading I like.
I know many users just love the Nikon colour science and the look out of camera.
If you want a particular look I suggest you have a look at your in camera settings, even cameras with limited profiles allow customisation so you can set things up as you like. Have a play and learn.