After reading some older blog posts, I found that you can use the mini.iso on an uefi system. All you have to do is extract the mini iso to a folder and chown it, then open the /boot/grub folder and mount the efi.img with archive mounter and then copy the resulting efi folder to that extracted folder. Then copy the contents of that folder with the extracted mini.iso and the efi folder to a fat32 usb stick. Then you can boot it normally in an uefi laptop.
When you extract the mini.iso, you won’t see the efi folder. You mount the efi.img to get at it. Then paste it. Then boot the mini iso in an uefi laptop/desktop, then install it and do as @manbutu had shown to get a pure ubuntu-unity-desktop.