You do NOT have a 2011. Those did not have an optical drive.
Since you said you have a 2 Hz CPU that mean you have an early 2009. Those do not have Internet Recovery. You are booting to the Recovery partition which was introduced in Lion. You Mac can go to the latest OS which is now Yosemite.
I recommend that you purchase the Snow Leopard DVD here:
http://store.apple.com/us/product/MC573/mac-os-x-106-snow-leopard
Then boot from it and format the HD and install and then fully update SL.
Then you can go to the Mac App Store and "purchase" the free Yosemite.
You can also order a download code for Lion for about $29. It will take a couple of days to get the code
http://store.apple.com/us/product/D6106Z/A/os-x-lion
Yosemite will be very slow with only 2 GB of memory. You can upgrade the memory to 8 GB (2x4 GB)
http://eshop.macsales.com/shop/memory/Apple_Mac_mini/DDR3
If you can't afford 2x4 I would get one 4 GB stick and replace one 1 GB stick
Lion is still very marginal on 2 GB
You can also replace the rotting HD with a SSD and that helps performance and is easy if you are already taking the Mac apart to upgrade the memory.The following are videos for how to replace the memory and HD
http://eshop.macsales.com/installvideos/mac_mini_2009/