My personal opinion is that if you want to do a system with a smaller overall number of strong classes (in the 4-7 range), you really want to move away from the idea of "main stat" for classes, and either have subclasses with a "main stat" or just remove the idea entirely. Then you can group tropes into classes by other identifying characteristics that you think they should share under the class umbrella.
4 classes:
Martial:
HD: d12
martial weapons
starting armor light+medium, option for heavy(or extra skills)
extra attack every 4 levels(4,8,12,16,20)
Gish/half caster
HD: d10
martial weapons
starting armor light+medium, option for heavy(or extra skills or extra cantrips)
extra attack every 5 levels(5,10,15,20)
half caster, 1-5 spell levels, new spell levels at class level 1,5,9,13,17
Adept:
HD: d8
simple weapons, option for martial(or extra skills or extra cantrips)
starting armor light, option for medium(or extra skills or extra cantrips)
extra attack every 6 levels(6,12,18)
2/3rd caster, 1-7 spell levels, new spell levels at class level 1,4,7,10,13,16,19
Caster/mage
HD: d6
simple weapons
starting armor none, option for light(or extra skills or extra cantrips)
extra attack every 8 levels(8,16)
full spellcasting, 1-10 spell levels(yes, add 10th spell level), new spell level at class level 1,3,5,7,9,11,13,15,17,19.