Your question is a little open ended. Getting started doing what? Is your interest robotics, device control, general electronics, software, etc, etc, etc.
That said, there are several general 'component' kits on the market that have a starter assortment of parts, (check Elenco, Sparkfun, Canakit) that can be used with your mBed.
You'll also want a solder-less breadboard to assemble your projects on. Since you're just starting out, get one with a base and the larger the better. I always end up starting a project on a bread-board I think is big enough only to have to transfer to a bigger one during development. You'll also want breadboard wire jumpers, get ones that have pins on the end, not just preformed wires (the preformed goes away after a few uses anyway).
If you're looking at this for general learning, experimenting, having fun with no preset goals I suggest you get a book or 12 that cover electronics experiments for fun (search Evil Genius on Amazon.com).
Most important, HAVE FUN
Hi All,
I just had a support request asking for recommendations for starter kits.
I found this blog article, but it is >1 year old, so I am sure more has come to exist.
If anyone has any further additions/recommendations to getting started kit, can you post it to :
http://mbed.org/blog/entry/mbed-Breakout-Board-and-Starter-Kits1/
Many thanks, Chris