My 5E ideal
A lot of good thoughts, but most seem to lack the punch of a whole new edition.
Table of Contents:
Obligatory what is roleplaying, how to roleplay, using dice, etc.
Creating a character
-Select a background and a concept.
--Sample backgrounds, concepts and how to build your own.
--Align your character's values (god, country, law, family, friends, self).
-Select your classes.
--Discussion of primary, secondary and tertiary classes.
---Primary is how you fight, short list of classes.
---Secondary is knowledge and socialization, short list of classes.
---Tertiary is the thin veneer of how you present yourself.
-Select your race.
--Discussion of what races are, sample races, the difference between fluff and crunch.
--List of sample races with fluff and standard crunch.
--List for choosing your own crunch.
--How to create new fluff and how to assign crunch to them.
-Assign your ability scores.
--What are ability scores and how are they used?
--Discussion for how all stats are useful for any build, if it suits your character.
--Str, Dex, Con, Int, Wis, Chr.
Character classes in detail, etc.
I move the steps of character creation around to reflect their actual importance. You start with the concept, then build the character according to it allowing for simple hack-and-slashers or nuanced politicians. The alignment system is a ranking of things you consider important, in order of importance. The current chaotic evil alignment would be (Self) and nothing else. A current lawful good might list (god, law, country, family, friends, self), putting his own needs last.
Each character is composed of 3 classes or concepts. Choosing Fighter from the first list does not constrain your options for the second or third. The roles of these classes do not overlap, thus there are no combinations better than others. The combat class would work much like a 4E class. The knowledge and social class would contain the skills and abilities to interact nonviolently, making rogues more of a secondary class. The third class is the glue and the role you present to the world, a swashbuckler, a noble diplomat, a savage; should be tied closely to your background; this class offers less in the way of mechanics but much more fluff.
If there are only 6 primary, 6 secondary and 6 tertiary classes in the first book, that would make for 216 combinations. It also means there is no need to make the savage wizard a new class, or the savage fighter etc.
Races would do away with the false options (or no options) of previous editions. If an elf wizard is mechanically better than a dwarf wizard, then the option to make a dwarf wizard is not really an option at all. Instead, the race you pick does not come with a predetermined package of bonuses, just a suggestion. You can pick your own bonuses, making all options viable. Alternate rules that allow the DM to set in stone what races get what bonuses. With the fluff separated from the crunch literally ANY race your DM will allow you to play is just as viable as any other, with no need for separate rules or supplements.
Stats would be much the way they have always been. However, the later-on mechanics will allow for more choice as to what stat you use with each of your abilities or skills. The fighter using Int as a prime stat is mechanically identical to the fighter using Str. As you gain abilities, you assign each an associated stat in a balanced fashion. You cannot have 2 strength abilities unless you have at least 1 ability for each of the other stats. Thus, the character that put everything into 1 stat will be very good at very few things, but a rounded character will be somewhat good at many things.
Feats I see as much the same as they are now, except that when you gain a feat, you can choose to spend it on your primary, secondary or tertiary class depending on what type of character you want and what type of campaign you're playing in.
Weapons. This is where many a sacred cow gets slaughtered. Three categories for weapons: one-handed, two-handed and ranged. You assign 3 scores to 3 qualities for a weapon. Great, good, poor. Damage, crit, specials. Two-handed weapons get a bump in these stats (a great damage might be 1d10, but 2d6 for two-handed). Ranged weapons get a further stat of range, which requires you to have a zero in either crit or specials. Then you just apply those mechanics to the weapon you would like to imagine your character having. Broadsword, chakram, katana, trident? All use the same basic rules. These apply to the way YOU use YOUR weapon. You and friend may both have longswords, but you use them completely different.