I've been searching online for the best portrait cameras, and they're very expensive.
I'm sure someone can give a tip on the best ones for those on a budget.
What I'm most interested in is taking photos with the right .mm to get the true faciall proportions, as we see them in real life. (which is why I can't do it with my phone, because it add so many distortion to it).
My guess would be something between 50 and 85mm depending upon your distance from the subject but that's in FF or 35mm terminology. If you go APS-C the numbers change to 35-56mm and with Micro Four Thirds they change again to 25-45mm. All figures being there abouts and distance to subject dependant etc.
What I'd recommend is a fairly modern mirrorless camera (and by fairly modern I mean something introduced within the last 10 years or so) because with mirrorless you get eye detect and the ability to focus just about anywhere in the frame and this gives you greater compositional freedom as you can place the subjects eye or whatever you choose to focus on just about anywhere in the frame. With a conventional SLR/DSLR you're possibly limited by the placement of the focus points which could well be in a rather tight grouping around the central area thus potentially giving you a problem or two if the main point of focus isn't in that central area.
Cost depends on which way you want to go, FF, APS-C or MFT and the focal length and aperture you want to use. Personally I like most if not all of a persons head to be reasonably sharp so I wouldn't be taking a tighter shot with FF at f1.2 and that would bring the costs down for me as I wouldn't need a f1.2 lens.
So, it all depends on the end picture you want. My normal thought process is to start at the end result and work back to decide the kit and the settings so I think being clear in your own mind is key. Think about what final framing and look you want and that will help to decide the settings and the kit capable of achieving those settings and that look.
Good luck.
PS.
Just on costs.
I used to have a Panasonic G1 and at lower ISO's I was impressed with the image quality and although I sold that camera years ago I still look at pictures I took with it, but as they're getting old now finding one which isn't sticky (the plastic goes sticky after a number of years) might be a problem. A G2 or G3 can be had for around £100 or less and the rather nice Olympus 45mm f1.8 (90mm equivalent in FF terms) can be found for around £100 or less. So, a G2 or G3 and 45mm f1.8 could maybe be found for around £150-£250. Other options are available

but I just thought I'd make the point that depending on the look you are going for and the image quality you want your entry point might not be an awful lot of money.