Reddit reviews Tai Chi: A Beginner’s Guide: How to Master The Ancient Art of Moving Meditation

The main thing is that you should see if there's an instructor nearby. In general, doing taijiquan is relatively safe, but there are some movements which may hurt your knees if the movement isn't quite right.

This ebook has excellent cost to quality ratio (the Kindle e-book edition is free). It's nice for filling in the background on the main styles and terminology.

So, there are a few different styles. Most common one is Yang family style, and within the different branches of what counts as Yang style, the shortened 24 postures form is probably the most common. If you really, really can't find an instructor, Ian Sinclair's video series on the postures can get you started here. There's also a few alright introductions into the shorter Chen forms on YouTube, but those do look like they just might be a bit piratey. For-pay, there's Ken Gullette's Internal Fighting Arts site (link) which offer a wealth of material, but if you rely only on master Ken (no, not that Master Ken) you'll essentially need Skype and/or a way to video yourself to get feedback.

There is also a wealth of literature; depending on your interests, there may be some literature which tells about the connection of the set to the traditional Chinese medicine theories or the applications embedded into the movements. (Though in the form, the actions are more or less mimed and applications may vary considerably on how the form is done.)

E: Added a note on Chen family style resources.