OS X internet recovery older version problem

I am using Macbook Pro Mid 2012 13" with 128GB SSD. The latest installed version of OS X was El Capitan which crashed during a Sierra upgrade.

Internet recovery mode worked somehow to land me to install download and install a new OS but it's Mountain Lion, which came installed when I bought the Macbook few years back However, it's rejecting to install on current SSD drive as shown in pic.

I have another 320GB HDD, so is this the only way to reinstall? First I do a fresh install of Lion on the external HDD? What I should I do?

What is a step by step procedure as all I want to do is run OSX on SSD drive but keeping all my older data. I can not afford to wipe it.

However, I did back up some of its backup onto my PC. If I install Lion the HDD can I then download Sierra and create an install disk to update/fix/install corrupted OS X on SSD?

Note: This answer has been updated because the comment below misunderstands how Recovery works. When your Recovery partition gets updated, not only will it run the newest version of macOS, but the installer gets updated to the newest version as well.

If a Mac shipped with macOS 12.3 or earlier, then Internet Recovery will install whatever version of macOS shipped on the Mac, even if the Mac had previously been updated.

If the Mac shipped with macOS 12.4 or later, or was upgraded to 12.4 or later, then Internet Recovery will install the most recent version of macOS that is supported on that Mac.

So if your Mac shipped with 10.11, and you updated to 10.12, then: Internet Recovery will install 10.11 Recovery will install 10.12

If your Mac shipped with 10.11 and you updated to 10.12.4, then: Internet Recovery will install 10.13 (or later) Recovery will install 10.12.4