what is the best way of groupping vowel sounds?
Long and Short vowel sounds
Lax and Tense vowel sounds
Back Front and Mid Vowels
Which grouping would be the easiest to explain to the students?
You can't choose from these groupings. Any vowel can vary along all three dimensions; four if you include close/open; five if you include nasalization; six if you include lip-rounding....
I think, from the point of view of teaching English, long/short would be the most easily grasped and the most useful for describing phonemes. But you can't hope to describe a vowel sound using just one parameter.