I did something one time, but don't have the project anymore. (Nothing too fancy though, just having pliers "crawl" across a desktop.) Any digital camera that takes sequentially numbered images can do it. (Which means pretty much all of 'em these days.) To avoid camera shake, having a tripod is the most important. Next is making it so that pressing the shutter button doesn't shake the camera. If your camera doesn't have shutter delay mode or a remote release, just about all cameras do have a 2s setting under the timer settings. So there's no excuse.

As for software? Any decent video editor should also be able to string sequential numbered images into video. Free software like Virtualdub even works great for this if you don't need to get fancy.

Some of the other stuff isn't as important or allows much more creative freedom. For instance you don't need much in the way of fancy lighting if you can slow the shutter speed, etc. Despite not being absolutely necessary, having a DSLR where you can set the camera to full manual may be a great step up. (Automatic cameras may do things with exposure metering or white balance that can make stop-motion flickery. It's watchable, but may not be an effect you'd want. Full manual setting makes it go away - with the caveat that you have to think more about lighting vs camera settings. Disabling autofocus also gives more control of direction.)

I'm willing to bet you have everything needed to do the basics. There's some other stuff like armatures and special puppets, but that's if you're really getting into it. (I haven't, but did read and watch videos because it's interesting.) And supposedly Dragon Stop-motion is really good software for compositing work relating to this. (I figure you can use PhotoShop even, but erasing some wires or rig from 100+ images? There's a reason why the specialized stuff was invented.)

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Barbequed Pixels?

Your friendly neighborhood Wings3D nut.
Also feel free to browse my freebies at ShareCG.
There might be something worth downloading.