Next week, I am going to buy a Raspberry Pi 3 and I want to buy a mouse and a keyboard with the Pi.
Can anybody please tell me if the Logitech MK235 works with the Raspberry Pi?
Really this is mostly an operating system issue, and not a brand-of-my-computer issue. Presuming you are using Raspbian or some other GNU/Linux variant, the OS kernel (which is what implements hardware drivers) is one which is used on tens of millions of normal workstations and laptops.
That looks like a pretty standard wireless keyboard/mouse combo ("Fullsize, durable, simple"). USB HID (human interface device) protocols are standardized, and anything like that will be fine. There's only a potential issue when you get into zany mice with 42 buttons and lots of special features that require a proprietary driver. That Logitech product does not fall into such a category. I've used piles of Logitech HID ware with linux over the years including wireless keyboard/mouse combos.
In other words yes, I promise it will work with the Pi 3.
Note that by default Raspbian uses a UK keyboard layout. Because of this you will notice a few keys don't print what they are supposed to. To fix this, when you first turn the Pi on, you should be presented with a program called
raspi-config which lets you set various options (if not, just run
sudo raspi-config at the command line). The fourth option of the main menu should be "Localisation Options". Choose that, then "Change Keyboard Layout" and select a US 104 key PC keyboard.