Playing slow and studying in detail the motions your fingers are making is never a bad thing when practicing. Slowing things down so you can order each finger to do exactly what it's supposed to do instead of some random "tries" is better for building muscle memory correctly and of course when things are slow, you can also spot wrong/unneeded movements more easily.
As for the fretting hand position... It's more than just a matter of comfort. Thumb-over and thumb-behind are two different positions used in different situations. There's no universal "correct" position. As you mentioned, thumb-behind is for better range of motion and putting your fingers more straight onto the fretboard (thus making applying pressure easier). Thumb-over is used primarily when bending strings and sometimes also for fretting/muting the bass string(s).
Mind that with thumb-behind you don't necessariy anchor your thumb in one position. Depending on the chords/notes you are playing at that moment, the thumb shifts and twists with the rest of the hand position, so that the thumb keeps the entire hand in balance while the fingers push onto the fretboard. It's like waving your arms around when standing on one foot: the thumb makes sure the hand stays in balance, while the fingers do their thing
