Question: What angles and long-side/short-side ratios give the most aesthetically pleasing and graphically regular isometric (squashed and flat side up) hexes, that additionally resolve to whole pixel sizes for several sizes when rendered?

Answer: 
Since you presenting the hexmap through an isometric view that shifts things around.

Here is the traditional version with horizontal hexes that are effectively squished in the vertical axis to make a pseudo-isometric look.

![hex view 2](https://i.stack.imgur.com/V3CdB.jpg)

This takes a different approach with the hexes that are rotated to present no vertical or horizontal lines.

![hex view 1](https://i.stack.imgur.com/gnfGr.jpg)

Either style can work, just depends on what you want to do, the primary direction players will move through the world, and how much you want to avoid zig-zagging.
By "flat side up", I assume you mean "flat side horizontal" (as "up" could mean either the edge itself points up or it "faces" up, i.e. its normal points up).

I experimented with both orientations for a game I developed in college. Personally, I found ["flat side vertical"](http://startreksupremacy.com/blog/galactic_supremacy.jpg) hexagons more pleasing on the eyes. I could certainly be in the minority here, but I believe Civilization V uses the same orientation, so I'm definitely not alone. If you're not dead set on using one orientation over the other, then I suggest you experiment with both. Since most of the [online resources](http://www-cs-students.stanford.edu/~amitp/gameprog.html#hex) I've found regarding hex grids use the "flat side horizontal" orientation, many equations you come across may require adjustments; [this site](http://playtechs.blogspot.com/2007/04/hex-grids.html) should help.

I built my project with a resolution-independent UI framework that performed device pixel snapping automatically, so I didn't spend much time tweaking the angles and ratios. I believe each of my hexes had a bounding box of 96 device independent pixels squared (96 device pixels on a standard 96dpi display with scale = 1.0). You should be able to derive the rest from the screenshot :).