This is a difficult question for me to answer directly because I long ago came to terms with the fact that the way I'd do D&D if it were left up to me wouldn't fly as D&D. And since I have the sense the know that, what I'd end up doing would be a compromise with what is necessary to fly as D&D, and thus I'm entirely the wrong person to do it. For one thing, I'd probably develop ulcers. That major caveat aside, here are some general things that I prefer:
- A unified vision. Or mostly unified vision. AD&D 1E has it. DCC has it. Some other derivatives have it. WotC products don't. The closest they came to a unified vision was 4E and even there they had multiple personality disorder running wild in their text. Follow through matters, of course, but with a committee calling the shots you put a fairly low ceiling on the big picture quality no matter how hard you work on the development and fine tuning.
- Ability scores that match the rules. If it were me, I'd change the ability scores to match the way it is played (Exhibit #1, your honor, on why I don't get the job.) But it also works to make it play with the traditional six. Either keep the tradition and work with it or not, but be consistent.
- Don't mix class and skill. It's either class-based or it is skill-based. If it is class-based, then maybe rethink the exact niche of "class" to something more like the original--the package of things that you signed up to play that has everything bundled in. But build the classes from the ground up with a set of abilities that makes them easier to customize for the campaign. In this view, there are two steps: 1.) The GM (perhaps in consultation with some of the players that are so inclined) builds the classes for the campaign. 2.) Then once play starts, you use what is in the class, same as it was in, say, Basic/Expert sets. I personally prefer skills-based in most games, but I think D&D should be the exception there (for too many reasons to list).
- In the course of labeling abilities, there might be some things that are akin to "skills" even in a class-based game. Calling them "skills" is a bad idea, because it skews people's perception of what should be in the list and how they should work. I'm not wild about "proficiency" as a name, but even it is better than skills. I don't have a good answer for exactly how to handle this part, though. My personal drift is to make "classes" somewhat more narrow but build multi-classing into the base engine. For example, in that view, "wizards" class levels don't give any fighting ability at all, but the default multi-class structure is such that most "adventurers" will at least dabble a little. I'm not unaware that such a design has its own issues, and pushes rather forcefully up to the edge of "Not D&D" territory. (You'll note that in order for this to work, multi-classing would be closer to the AD&D model than the 3E model, but neither is a good fit as is.)
- I'd make a similar argument for race/culture/background, though in a truly flexible class-based game where the classes changed by campaign, I'm not sure it matters as much.
- Make the abstraction levels at least somewhat consistent. For example, if there aren't going to be that many difference in weapon properties, then a list of weapons similar to Basic D&D is not only fine but better than a longer list. If equipment in general is simplified, then you need that shorter equipment list. Likewise, if you are going to have more details in equipment, then probably some plausible encumbrance system, economic system, etc. is needed to go along with it. Ideally, there would be some ability for each group to shift the abstraction a little, but it would be presented in a handful of coherent rules packages. You don't care about all those details? Here's your short equipment list, some guidelines on GM eyeballing encumbrance and wealth, now Go! You do care about that, here's a more detailed way to handle all that stuff. You'll get the occasional person who cares enough to mix and match and work it out, but I'd rather have 2-4 reasonable sets of rules that work well together within each set, than a system of disparate parts with several options per part and the (inevitably mistaken) claim that they all work together.
- I only have a handful of negative preferences on D&D art. If it were up to me, I'd turn that over to a talent art team with the direction to "surprise us" as long as it doesn't look like (my personal short list of artists that are way over used). My dream art package would have a subtle nod to the Impressionists with a fantastical slant, but somehow I don't think that is a popular direction.