Reference for the Security Analysis of Ring-LWE Can someone please share a link of any research paper or web-page analyzing the security of Ring-LWE? Essentially, how should I choose my parameters to get security equivalent to 128-bit or 256-bit?
You should visit the Homomorphic Encryption Standardization web page. There you can find Homomorphic Encryption Standardization.

Also, there is a workshop The Second Homomorphic Encryption Standardization Workshop there you can find this document 


Homomorphic Encryption Standard see section 2.0.3


I hope, all this will help in your research.