Well you won't need the Mac Pro unless you are planning to do some sort of really high end rendering or are planning to edit custom video for your website with Final Cut or something. But if you had those kinds of specialized needs, you probably wouldn't be asking.
Mac Mini will definitely be adequate to the task, you'd probably be fine with the dual-core i5 but the quad-core i7 is such an upgrade, that it is probably worth looking at.
If your budget allows it, better to look at the 27'' iMac though. $1800 is a bit overkill for web development but understand that a great deal of that sticker price is going into an exceptional monitor and even if you saved by going the Mac Mini route, you'd want to invest in a really good monitor anyway. The Mini is also two years old, whereas the iMac is using newer technology.
The two biggest things you are going to want to invest in are RAM and a decent monitor since you'll be staring at code all day.