Canon Powershot A720 IS. Works a treat.
There is quite a lot of wank talked about miniature photography - sometimes by me

The critical thing you need, IMHO, is a camera which lets you set the shutter speed manually. This is something you get on pukka SLR type cameras, but not on cheap digital cameras (<£150.00 GBP) as a rule. But many of the Canon Powershot cameras have this feature, so look out for it.
It means that you can adjust the shutter / exposure to a slower speed. Which means that the camera's digital eye gets longer to look at your shot and get everything into focus.
This is particularly important with miniature photography, because if you're taking a pic of several figures in a group, you want them all to be in crisp focus - not just the one in the middle.
The other things you need are much more common on almost all digital cameras - a 'macro' feature (basically a close-up setting for shooting small stuff close-up) and a timed shutter release, so that you can set up the shot and then step away from the camera and let it do its stuff, thus avoiding the wobble which bedevils the pics of the inexperienced miniature photographer.
You hear a lot about 'white balance', but I've never paid the slightest attention to this. Every photoshop programme gives you the option to automatically adjust contrast, exposure and colour balance, so just run your pics through that and you don't need to worry about white balance.
You do need to get them unblurry / wobble-free and in-focus though. So macro, timer and manual shutter speed adjustment are the things you absolutely need.