Other races and classes aren't "essential" to what people think of as D&D, but I would like to see variants of:
Barbarian. Basic-attack-focused barbarian. You need to make the rages special to differentiate them from slayers. They'd be martial and primal, so depending on which powers you select you can choose to stay wholly martial, or get some magical enhancements.
Agreed. It could even be mechanically very similar to the slayer, but with (at-will/encounter) stances that reflect the rages. These would provide big hits, damage reduction, or great mobility at the cost of defenses, or even tactical control (for instance, dealing damage to any ally ending a turn next to the barbarian).
Bard. Some sort of 'sustain minor' musical powers.
I like it. The Bard also should be a secondary controller. I'd like to see lots of aura buffs and ranged control effects. All sustained with minor actions (and, preferably, most At-Will).
Monk. Simply make it basic-attack-focused, but add a feat that lets unarmed strikes be as good as martial weapons, then give the monk that feat for free. Give them all sorts of special movement options and encounter powers, but no dailies.
Yes, but they should also have secondary controller-type effects, especially things like prone and grab. Again, stances are an obvious fit (although movement tricks would work well, also).
Psion. Not quite sure how to do this one. We've already tried the power points mechanic. We could try something new, like have a few standard action at-will powers, a few encounter powers, and a couple minor action at-will enhancements. Whenever you use another power, you can spend a minor action to enhance it. Maybe. I dunno.
In general, I like it, but I think it would make more sense to have a few enhancements as encounter powers, rather than at-wills. Then, just use them to enhance a handful of at-will powers.
Sorcerer. There's currently no ranged arcane striker in essentials.
Artillery. The Sorcerer should be straight-up focused damage from range, lower-accuracy AoEs from range, and cover-fire, no controller effects, whatsoever.
Swordmage. Basic attack-focused swordmage, but your melee basic attacks can work at range. Your aegis still marks enemies, but you don't teleport over to attack; you just attack from range. And you keep daily spells.
Marking things at range can be fun.
Warlord. Basic-attack-focused warlord. Various maneuvers that the warlord performs to lead the rest of the party into battle.
I would want to see lots of at-will auras that buff allies or grant extra actions.
As for races, eh, I suppose they could do gnomes, goblins, minotaurs, orcs, and some sort of avian.
I care a lot less about races, but I
would like to see the gnome (particularly the tricksy 4e version). Oh, and some sort of construct race, such as the warforged.