The transition from Windows 7 to Windows 8 took me about two days to figure it all out and get comfortable with how it all works. With 8.1, it's a bit more easier for new people to figure out due to them adding that little windows icon in the bottom left where the start button used to be, but in 8, it was still the exact same thing, just there was no icon there to click on and you just moved your mouse to the bottom left and a little window popped up to bring you back to the start screen.
In a nutshell, the best way to wrap your head around 8.1 is that the Start Screen is just the Start Menu covering the whole desktop.
"Classic" mode is just a play on words really, as the "Classic Desktop" is the only desktop there is in the OS and 95% of everything you do in Windows 8.1 is on the Desktop just like when you used XP, Vista, 7, etc.
When you first start up Windows 8, you are presented with the Start Screen.... on that Start Screen there is an icon for "Desktop"
Click on that and you're right back where you left off in previous Windows OS's.
The Start Screen is mostly for any Apps you download from the App Store or XBox Game Store, while all your regular programs operate completely on the Desktop like you're used to, so transition in that regard is pretty quick and easy. You can either pin your programs on the desktop or the taskbar like always, or you can pin them on the Start Screen (which just loads them on the Desktop anyways)
When Windows 8.1 first loads up on your new computer, it will present you with a very quick tutorial on the extra little things it does, like the options/menus on the right side of the screen and toggling through the "Apps" on the left.
If you installed a program or app on your system but there was no icon on the desktop or start screen added, simply go to the start screen and when it is up, simply start typing out the name of the program or app and you will have a quick pop up of that program where you can then add an icon on the Start Screen or Desktop or simply run it.
My wife first didn't like Windows 8 when I first got it and it took her a little longer to figure it out than I, but after about a week she actually liked it more than Windows 7. Her mother also bought a Windows 8.1 laptop. I gave her a crash course on the basics and she has never had an issue with the OS and figured it all out pretty quickly for what she does with her computer.
One difference you will notice with Windows 8.1 compared to Vista or 7 is performance. Windows 8.1 is a lot more optimized than the previous OS's and doesn't use as much resources as Vista/7. After I upgraded my Windows 7 system, I noticed the OS boots withing seconds rather than almost a minute beforehand.... my programs like Photoshop, Illustrator, etc. all load faster and perform a bit better too. My games on Steam also load faster and I was even able to bump some graphical settings up ever so slightly due to more resources freed up.
Anyways, within the next couple of weeks, Microsoft will be launching the developer preview beta of Windows 9 (Threshold) which is basically Windows 8.1 but with some modifications based on customer feedback.
For starters, the Start Screen is switching back to a modified Start Menu which will be a combination of the Start Menus of Christmas Past and the current Start Screen.
Windows 9 'Threshold' Update Leaked in Purported Screenshots, Video | NDTV Gadgets (external - login to view)
Windows 9 Das neue Startmen in Aktion - YouTube