This can be a very personal choice As you start don't know even where to start , the list will and can change for you. Some are FAA type things of which there is no substitute (except free on the Internet) .
AND you do not need all of this to start in fact you should wait till you find a school and instructor to buy anything as sometimes they have packages available.
Airport Facility Director
plotter - variations of this exist
E6B - a slide ruler used for navigation calculations there are electronic versions
Practical Test Standards - very good to know to what level you will be tested
Airplane manual - you should have a copy at home to study
checklist - some schools have one that is always in the plane, always have your own just in case
fuel tester - see above comment
kneeboard - it is like a desk (but on your knee) some use a clipboard which does the trick too!
FAA flight training manual
FAA regulations and Airman's Informational Manual
a bag to carry all of this , you don't need a fancy flight bag maybe a book bag or backpack
Again your own instructor may omit and may add things to this list ,as for me I think the following are important also...
DVD private pilot course - these are an amazing way to save money as they will show you what you have been reading. You will see the maneuvers on the ground which is GREAT, you will know what to expect , I believe having this is a big time and money saver. Many even offer a guarantee that you will pass your written, practical and oral test..how can you beat that? These can act alone or supplement your ground school, it depends on how you learn. http://www.sportys.com/courses/private.cfm## is an example.
Rod Machado private pilot book - a very easy to read book that adds humor and grabs your interest.
Membership to AOPA
Subscription to Flight Training magazine - a magazine for flight students and instructors
except for the last two things everything is available at www.sportys.com there are many pilot shops and ebay is another great source
Fly at West Valley Flying Club!