If you want a TV that is compatible with the remote, then you will need to opt for a Samsung model.
The smallest compatible Samsung TV that is available is 24":
Yes, there are indeed universal remotes that you could use to control both the LG TV and the Samsung recorder:
Yes, the universal remote will work for both devices.
Yes, the Samsung BD-H8500M recorder has a built-in 500GB hard drive so you don't need discs.
You are very welcome :)