Any way in OS X to use a keyboard shortcut to switch to a full screen application?
To do this: push control and &lt; or control and →.

You can slightly change the functionality if you have "Automatically rearrange Spaces based on most recent use" checked or unchecked. (System Preferences > Mission Control)

There is no other way to do this that I know of. I have used a few third party apps. I am sure there exists some third party app somewhere that does it. I've heard that Witch makes the window switcher similar to Windows style, which might achieve the exact results you are looking for, but might not. It costs $15 as of today. It just doesn't mention fullscreen in its advertising, though it has a ton of options so it's possible it covers this.

Honestly, you can't expect much better from OS X. Look at what you're stuck with:

Switching between applications in OS X is command + tab and arranges apps by most recent. Switching between windows within an app is command + ` and arranges windows sequentially. With control + ←/→ and the "Auto rearrange Spaces..." unchecked, you can get the sequential switching similar to the way OS X handles window switching within an app, which is a poor way to do it, but at least there is some kind of precedent.

I have a lot of gripes about switching between applications in OS X. I don't like that there is one keyboard shortcut to switch between apps, one to switch between windows within an app, and one to switch between spaces, and they have different orderings. I want one to switch between everything. I also hate keyboard shortcuts that include an arrow key, like this one. That defeats the purpose of having a fast keyboard shortcut: I still have to move my hand, might as well use the mouse. I am strongly considering switching to Windows 10 this year now that it will include bash. I use keyboard shortcuts for almost everything and Windows does it better, not to mention that I honestly think Windows software looks better.