I can only really account for my tastes, to be honest, rather than provide a definitive answer for the OP.
Most of the key elements have been highlighted:
- d4, d6, d8, d10, d12, d20
- Class, Race (Culture?), Levels, Experience points.
- Strength, Dexterity, Constitution, Intelligence, Wisdom, Charisma (rated 3-18).
- Dwarf, Elf, Halfling, Human.
- Fighter, Rogue (Thief), Wizard (Sorcerer?Mage?), Cleric (Priest?), Ranger, Paladin, Bard, Druid, Monk?, Assassin?, Barbarian? Witch/Warlock?? Psion???
- Alignments - Lawful, Good, Neutral, Evil, Chaotic - or combinations.
- Spell slots, spell levels and fire-and-forget casting.
- Abilities primarily defined by Class, and Saving Throws.
- Attack rolls, Armour Class, HP,
- Pseudo-medieval fantasy implied. Otherwise, general
Preferences beyond this would be:
- the freedom to play abstractly without miniatures if you want.
- No overt mechanical typing or terminology - Tactical Roles, Power Sources, Healing Surges, Common/Rare Classes etc.
- Backgrounds and Themes (Good Idea!)
- Abilities generated by random dice or points spend.
- 'Cultures' instead of 'Races' - incorporating a variety of Dwarf, Elf, Halfling and Human cultures. That way you would describe your character by Class, Culture, Background and Theme. 'Barbarian' would be a Human Culture.
- Optional alternatives to Alignment, including the option to ignore it.
- Light skills list - based on Ability scores.
- Some cross-class feats/abilities - but not overwhelming lists.
- Feats generally based upon Class-only lists - but again, not overwhelming.
- Sensible levels of HP, for each Level.
- Multiclassing and Prestige Classes, without an over proliferation of Base Classes (absolutely no more than 15 or so in total. 13 above would be about right, maybe as low as six - see below).
- Theme and Background (good idea).
- Levels 1-30.
- Some customizability to adapt rules to other settings - space opera, western, etc, without being overtly GURPS like.
- Classes based on Primary Abilities - Fighter (Strength), Rogue (Dexterity), Ranger (Constitution), Mage (Intelligence), Priest/Druid (Wisdom), Paladin/Bard (Charisma).
- Fighters would be the most customizable Base class for warrior types, with the most options (Feats?) to develop their own style of combat, and being an umbrella for any type of warrior. A 'Monk' would be a type of Fighter, designed for unarmed combat.
- Rogues would be the most customizable skills-based Class.
- Mages would likewise be the most customizable of the spell-casting classes, and given multiple options to develop their own style of magic, including alternative systems.
- Rangers would be the most adaptable travelers and survivalists, including healing abilities.
- Priests/Druids and Paladins/Bards would be designed clearly on Cultural grounds.
- Less overlap between Classes in terms of Abilities - no spell casting Rangers or 'Sword Mages', etc. Multiclassing and/or Prestige Classes should be required to cover other options.