Which model of computation to simulate to prove universality? I am starting out in theoretical computer science.

I have a model of computation based on observations of auto-associative memory in the brain.  I believe (with little evidence) that I can do anything in this simple model.  I understand the primary way of proving universality is to show that your model can simulate another universal model, especially a turing machine.

I would like to request the following information:


References to clear and easy to follow proofs of universality of a computational model, graspable by an able beginner such as myself.
Guidance as to what model would be easiest model to attempt to simulate.  I imagine the answer to this may be 'it depends'.  Currently it appears my model bears some semblance to lambda calculus.
There's a comprehensive treatment of different Turing-complete computation models and proofs of their equivalence in Martin Davis, Computability and Unsolvability. Some of the most popular systems are described, including Turing-Machines, Post problems and general recursive functions.