Hello,
You are asking about multiple environments here.
I would say when it comes to the various indicators Gnome is the best in terms of accessibility.
To navigate over the parts of a gnome desktop you can use ctrl+alt+tab and ctrl+alt+shift+tab respectivelly.
When you login into gnome session you will land on an empty workspace with no apps running.
If you try out navigating with ctrl+alt+tab in this state, you will recognize you can move between top bar and windows.
The top bar with quick settings and indicators is visible all the time.
In the pannel reported as windows there are all the application windows. You can switch between individual apps by pressing alt+tab or alt+shift+tab respectivelly. You can switch between multiple windows of the current app (e.g. multiple browser windows) by pressing alt+grave or alt+shift+grave (the key in a upper row of keys - immediatelly above the tab key).
When it comes to navigation on the top bar on the Gnome desktop I think you will recognize it features similar navigation paradigm to the menu bar known from your Microsoft Windows machine. You can use left and right arrow keys to navigate over the available menus. You enter the menu by pressing the down arrow. In the menu you can usually navigate with up and down arrow keys. You can expand or collapse expandable controls or manipulate the sliders with right and left arrow keys. You can activate items or toggle checkable items or select radio items by pressing the enter key. You can toggle the toggle buttons by pressing the space bar key. When you expand a collapsed control, you can press down arrow to jump to its first child and then you can continue navigating with left and right arrow keys.
On the top bar you will find an Activities toggle button, current application window menu (only applicable to GTK+3 based apps - analogous to F10 menu in Mate and other GTK+2 based environments), accessibility menu and a system menu with indicators, with logout and shutdown buttons.
Instead of alt+F1 menu known from Gnome 2, Mate and others, Gnome 3 features so called activities overview. You can get to this overview either by pressing the super key alone, or pressing alt+F1 or by going to the top pannel and toggling on the Activities button there.
When the overview is showing the application windows are all minimized and a windows pannel displays window chooser. You can see all the application windows represented as buttons here. You can press arrow keys to navigate and enter key to switch to chosen window.
When the overview is showing you can move to even more pannels by pressing alt+ctrl+tab and alt+ctrl+shift+tab e.g. dock, Search and Applications as an addition to top bar and windows.
Dock is a row of icons to your favorite apps and running apps. You can navigate over the icons by pressing up and down arrow keys. Individual icons do usually have a popup menu you can inwoke by pressing the applications key (the key to the left of the right ctrl key on most keyboards). The popup menu contains some contextual items for example you can open a new web browser window, create new text document and similar. It's app specific. Also you can add or remove an app from favorites. Favorites are the apps displayed first on the dock. Ordering of these apps is not accessible via keyboard however they are ordered as you are adding or removing them from the favorites using app specific context menus so for example if you do have Web as the first item, you will hit remove from favorites inside its context menu, then find it again in the list and add it to favorites it will be added to the end of the dock. The last item on the dock is a toggle button you can use to show or hide the applications view.
Applications view is very similar to the dock except you can use all four arrow keys to navigate over the apps arranged in a grid. By default frequently used apps are shown with ability to toggle the view to display all aps on the bottom of this view. Popup menus can also be inwoked for the individual apps.
Search has a text entry where you can type your search query. In fact if you don't require ability to edit the content of this text entry there is no need to navigate to it because you can just open up activities and start typing the query. You can search for apps, documents, files and possibly other types of content this way because individual apps can plugin into this mechanism.
There are some predefined keyboard shortcuts. You can browse over the list of keyboard shortcuts somewhere in the Settings -> Keyboard. Those include for example super+a to jump directly to the list of applications from anywhere. Or there is super+m to jump to the notifications also reffered to as system tray. This is also on the top bar however I think there is no other way on how to get into notifications besides pressing super+m keyboard shortcut.
Also there is an usefull wiki page here on the gnome site you might like to read to find out more gnome features:
https://wiki.gnome.org/Gnome3CheatSheetI hope you will find this usefull.
I have never used alt+ctrl+esc within Mate and I do also have mixed results using pannels on Mate desktop. Still I am using Gnome more it's why I have chosen to describe it in more details so you can also get some good use of it.
