Training with an Instructor is the best way to ensure you are performing the moves safely for you, especially if you have an existing health condition.
Youtube is a great resource, but there are also plenty of poor or inappropriate examples of T'ai Chi on there (you don't have to be an expert to post a clip online), so do check the feedback before trusting any videos.
The "Lady in Pink" is well known for the 'Simplified' 24-form; the most popular across the world
(don't let her great flexibility put you off ~ she has trained for many years!)
This Shibashi 18 posture Taiji Qigong video is by Shan-Tung Hsu's Hong Kong "sister".
(Chinese with English descriptions. 1st 20 mins = breakdown, 2nd 20mins = flowing movements)
Here is a (50 min) talk by Dr Paul Lam on his "Tai Chi for Health Program"; Founder of the 'Tai Chi for Arthritis' form and clearly a fit 60+ year old in 2009 despite being an Arthritis sufferer from the age of 13. www.youtube.com/watch?v=co1uxOFJ8Mc