Currently I have a laptop with Win 10 Home 64 bit, buy me a new one soon. Can I take the operating system with me and buy the new computer without it or not?
The question can't be answered flat rate.
If your Windows license allows it, then yes, otherwise not.
Standard with licenses, which one acquires with the PC is: It does not work.
If Windows 10 was preinstalled on your other laptop, it's probably hardware-bound and unfortunately can't be taken.
You have to buy a new license or use GNU / Linux (for free).
On the computer that lacks the license, I would install the free Linux Mint. "Download Mint" provides you free of charge and legally the best equipped operating system. Mint is easier to handle than the non-free Windos.
Linux does not need a virus scanner, Office is already there. Maybe Win will not be needed anymore.