If you don't use full-screen-as-a-separate-space, it only requires a little tweaking of default parameters to get something usable, even if not to your liking. (By the way, is there some setting so that the default action is zoom and the alt/option one is full screen ?)
In settings -> mission control, deactivate automatically rearrange spaces, which is probably why you think that some applications appear on multiple spaces: actually, it's only on a single space (by default), but the spaces keep being rearranged.
If you want a space to span all monitors, I guess you can do it here too, but I'm a fan of distinct spaces on distinct screens, a feature I had 15 years ago on X11 (but which implied the inability to move windows between screens). Note that GNOME 3 does (did?) something "interesting" by default, which is a single desktop on the secondary screen, and virtual desktops on the primary one. Probably useful on laptops in presentation mode. (Is the default over-ridable) ?
In settings -> keyboard -> shortcuts, activate Mission control per-space bindings, so that you can swap between spaces with ctrl-(number). The catch is that you have to organize your spaces by task. You can then bind applications to some spaces. You can do that by alt-clicking in the dock and looking in options. Older versions of Mac OS X with Spaces (instead of Mission Control) had a list of assignations.
The space selection widget is gone though, if you won't use shortcuts, it's F3. Each space is rendered as a thumbnail on the top, you could choose a different background for each space if it helps you. The bottom part is all of the windows in the currently selected space. What is not very obvious is finding the currently selected space, depending on your color scheme: the white border is not very visible on white background.