You can install up to macOS 10.13 High Sierra on a 2010 laptop.
I highly recommend you create a bootable macOS 10.13 USB installer now while you still can since there have been a lot of reports on this forum of people saying it is no longer possible to install macOS through Internet Recovery Mode. Here is an Apple article with instructions for creating a bootable macOS USB installer (article includes a link to download various macOS installer as well):
Create a bootable installer for macOS - Apple Support
Even with macOS 10.13, none of the major browsers are still supporting this old OS so accessing the Internet is going to become more difficult as time goes on.
Another option would be to install Linux Mint on the laptop which is a great way to extend the useful life of older computers. This gives you a non-Apple OS which is up to date and has access to the current versions of popular browsers. It also includes LibreOffice which provides the ability to access MS Office files along with lots of other open source apps. The only downside is most proprietary third party apps are not available for Linux, but they also are not available for such an old version of macOS either.
You can test out Linux Mint by selecting the "Live" option from the Linux Mint installer. It will be extremely slow since it is booting & running from a super slow USB stick, but it will give you an idea of what it is like. You can also install Linux Mint to an external drive if you want to fully test it out (this won't affect the macOS installation on the internal drive).
Again, make sure create a bootable macOS USB installer before you do anything so you have a way of reinstalling macOS.
FYI, here is an Apple article with instructions on how to prepare a Mac for sale so that you disassociate your AppleID/iCloud from the laptop:
What to do before you sell, give away, trade in, or recycle your Mac - Apple Support
If this laptop uses a hard drive, then I highly recommend you first enable Filevault and let the encryption process complete so the data on the hard drive is inaccessible, otherwise you would need to use the Secure Erase feature of Disk Utility to write zeroes to the entire hard drive (both of these processes can take a while). If the laptop is using an SSD, then just a simple erase is enough to destroy the data on the SSD.