What hardware will be sufficient for FCP X? Starting from nothing

I'm going to be picking up a Mac for making commercial shorts in FCP X (720p and HD, 3-5 minutes long generally), and trying to get my head around which of the current offerings would be sufficient for the task. Budget is a concern, so I don't want to automatically just go with the best or most professional-level option. I haven't worked in the Apple environment at all, I'm thinking about converting from PC.

So far I've narrowed it down to these options.. which is pretty broad, so I'd appreciate the community's feedback. If this is in the wrong section, I apologize ahead of time.

1. Mac Mini 2.5 and buy RAM/monitor/keyboard/mouse
- About $1000
- Not sure if it will be powerful enough
- I don't have a monitor/keyboard/mouse because all my monitors are being used in my current setups, so it has to be priced into the cost of the system

2. Mac Mini 2.3 and buy RAM/monitor/keyboard/mouse
- About $1200

3. Macbook Air 13" with RAM upgrade and buy a mouse
- About $1350
- Can be used on the go, which would be pretty awesome
- Will be stuck with a small screen, might have to pick up a second monitor

4. iMac 21.5
- $1300
- I believe it's less powerful than #2 and costs more? Not sure whether this is a good choice.

5. iMac 27
- $1800
- Way above budget, but leaving it on the table in case someone has a really strong recommendation to make.