Measure the seat, not the room
Screen size depends on how far you sit, not on the size of the room. The SMPTE guideline asks for the screen to fill at least 30 degrees of your view. THX recommends 40. From 10 feet that's 74 to 100 inches.
Bigger than you planned is the usual answer: almost nobody returns a TV for being too big. Below 20 degrees a TV starts to feel like a window across the street.
Questions
How high should a TV be mounted?
The middle of the screen at your seated eye height, usually about 42 in (107 cm) from the floor. For a 55 inch TV that puts the bottom edge about 28 in up, for a 65 inch about 26 in.
How high is too high for a TV?
When your neck tips back more than about 15 degrees to see the middle of the screen. Under 10 degrees is comfortable for nightly watching.
Is eye level the centre or the bottom third?
Most guidance says centre at eye level. THX suggests your eyes line up with the lower third of the picture, which raises the middle by a sixth of the screen height. Eyeline does both.
What size TV for my distance?
Enough to fill 30 to 40 degrees of your view (SMPTE and THX). From 8 ft that's 59 to 80 in, from 10 ft 74 to 100 in, from 12 ft 89 to 120 in.
How high to mount a TV over a fireplace?
As low as the mantel allows, with a tilting mount angled down toward your seat. Check the neck angle: over 15 degrees for nightly viewing is hard on the neck.
Where do I drill?
If the mount holes are in the middle of the TV back, the bracket's middle goes at the centre height. If not, measure from the top edge of the TV to the holes and put that in; Eyeline gives the hole height.