When it comes to footwear for training, the Vibram FiveFingers are ideal. Not only are they flat (and the absence of a heel will have an immediate impact by itself), they encourage your feet to really engage themselves in the running, lifting and climbing.
It really is like a controlled barefoot training session.
Once your feet become used to them (and this could take hours, days or weeks depending on your current footwear), there are several long-term benefits. Improved posture, balance and so on. It really does get better and better.
Where To Get Them
This is one type of footwear that I'm entirely happy buying online. The sizing depends on the length of the foot (details here), and is flexible enough to cope with minor variations from person to person.
In Australia, they're available from :
NB : this is where I bought mine, and the service is superb. Overnight delivery; no problems at all.
In the US, swing by the main Vibram Five Fingers site. I've also received good feedback on stores like Kayak, and of course, Amazon.
Outside these countries, your best bet is either a local shoe store, or a major online retailer (such as Amazon, or the main Vibram site). Whatever your experiences, I'd love to hear them.