I'll probably give up on re-writing the whole system; there are just too many spells to consider. I'll just have a version to introduce new players into the game, with a few DM tips, and I might use it for my own games (since I don't like spell slots, etc.). As always, I think I'll make most of these things optional. Except, maybe, for spell points.
Without further ado, using 5e rules with some changes defined in this "Minimalist D&D" series, here are my three classes:
HD: 1d10 per warrior level.
You get an extra attack at levels 5th, 11th and 17th.
You get +1 to hit, damage, and AC. With your favorite weapon type (swords, maces, spears, polearms, unarmed, grappling, etc.), you get +2 to hit instead.
With every new level after the first, you can learn a cool battle maneuver (probably with a bonus action or reaction) or power (rage, an improved second wind, re-roll a saving throw, making an extra attack, tripling the damage of a crit, etc. - each one costs one HD), or raise one ability score.
HD: 1d8 per expert level.
Starting at 5th level, when an attacker that you can see hits you with an attack, you can use your reaction to halve the attack’s damage against you. At level 11th, you add 1d6 when rolling any skills. When you reach 17th level, you can take two turns during the first round of any combat. You take your first turn at your normal initiative and your second turn at your initiative minus 10. You can’t use this feature when you are surprised.
Choose one broad skill (observation, nature, arcana, craft, etc.) - you have advantage while performing this skill. You can spend one hit die to give yourself advantage in other skills.
You add 1d6 times half your level (round up) to your sneak attacks.
With every new level, you can choose a cool move you can make with a with a bonus action or reaction - hide, help, disengage, give yourself advantage in your next attack, etc., or some cool power (usually related to movement, hiding, or spell) you can use by spending HD, or raise one ability score.
HD: 1d6 per spellcaster level.
Spells/cantrips: start with three, add one per level. Pick a spell list from one of the existing classes, and you must use the same
Free spell: you can cast one spell per day without using any spell points or HD.
Spell points: you have one spell point, plus one per level. They refresh at the same time and at the same rate as HD. It costs one SP or HD per spell level to cast a spell (smite and turn undead are now spells, BTW).
Spell levels: the maximum level you can cast is equal to half your level (round up).
Feats/ability score raises? Maybe a few on even levels. Yo'ure already getting plenty of power on odd levels.
No saving throws (you probably roll against the target's abilities). No skills (only skill sets the expert can get). No fighting styles. No weapon or armor restrictions (if you can pay for it and carry it, go for it). We are ditching EVERYTHING but abilities and a few features.
And that's about it. Let me know if anything seems unbalanced.