I know a lot about calibration. (I’ve just prepared material for Discovery for delivery.)
Viewing calibration falls into two categories:
1) Basic calibration
A basic calibration disc or file which you use on your display device get the correct black and white levels. And also Turning off electronic features such as auto motion / adaptive black levels and all that rubbish.
That’s 75% of the battle.
2) Advanced Calibration. (Trickier)
An advanced calibration will look at the above plus tracking your greyscale, setting your colour targets etc. For that you will need an X-rite i1 or Spyder variant.
Films in particular are colour graded in light controlled environments with a lot of skilled emphasis on reference colour targets -so the Director can give you a precise image.
You can recreate that at home with most modern display devices and a lot of practice. Ideally you also need light control too.
We have calibrated monitors here for studio/production work – and back home I have a projector set up to REC 709 which gives you a decent HD (not perfect) representation of what the film-maker intended.
Cinema output is P3 standard and home stuff is just starting to get there.
You should shoot for REC-709 or sRGB and a Gamma of 2.2 – 2.4
Most display devices come with out of the box profiles – most aren’t really that accurate but they’re better than nothing.