Let's answer your question seriously for you. A Prop is what you make it out to be. Technically a pad of paper is a prop but it does not look as magicky as a yellow wooden box with a chinese character or a dragon painted on the side which DOES look like a magic prop.
Esential equipment would depend onw hat you require for the effect. While some may prefer to use a peek wallet, some may prefer to use an envelope and a card and others may prefer to use merely a piece of paper to accomplish the same effect. (I hope that makes sense). Many will say that a "nail writer" be it a band, undernail, thumbtip type is essential while some may say they are not. It really all depends on what you wish to do and how you wish to accomplish it.
If you were to read say "Stunners Plus" by Larry Becker you will find many "mental magic" effects. Brilliant ideas and principles to be learned within those pages and many years of readings will be had by this tome and some of the effects contained within it's pages are very "propy" and some are not. (Some consider a deck of cards propy as well). However if you were to read Bob Cassidy's "Art of Mentalism" you will find that aside from a small day planner, some cards, paper and a couple of pencils you require nothing else to produce miracles. Both are amazing books which contain outstanding material but both are very different as is their authors both as person's as well as style. (Those that know these two giants will know excatly what I mean by that,all good too)
So there really is no "essential" props or techniques for that matter. All boils down to how much of a purist you are and what you want to do. Since you have read the two classic i do suggest that you read the two aforementioned books (although Cassidy's has 2 of the Art of Mentalism and you should read both.) Cassidy's "Principia Mentalia" should also be read.
Once you have read those you might try to move out and read varied books such as "Peek Performances" and "Peek Encores" as well as the other books by Richard Busch - all considered essential reading by established mentalists. "Paramiracles" by Ted Lesley, Barrie Richardson's "Theatre of the Mind", all three of PUNX's books will show you how "theatrical" you can be in your presentations.
"Prism" by Max Maven will provide you with a great read as will "Magick" (all four volumes) and "The Encyclopedic Dictionary of Mentalism" (all 3 volumes). T.a. Waters "Mind, Myth and Magic" is chock full of great ideas, "Al Koran's Legacy" by Hugh Miller was just reprinted and will show you some ideas on the shoulders of a mentalism giant. There are many more too but the ones I have mentioned will show you a variety of styles, principles and ideas.
Magic and Meaning by Burger/Neale would be an assett to performing mentalism as would "Maximum Entertainment" by ken Weber, more so in your presentations as opposed to tricks. I hope this helps,
AB Stagecraft http://www.mindguy.com/store
Where mentalists come for unique material