Any modern Mac with 4GB RAM is able to accommodate multi-track recording. There are many other aspects that might impact on your decision to choose from iMac, Mac mini or MacBook Pro and require throwing money on extra devices:
1. External audio interface. Firewire-based one is better, because it provides a constantly-rated stream. Personally, I use Edirol FA-101 it is 10-channel device with excellent sound. Note that new iMacs, Mac minis have FW800 interface only, so youll need a converter FW800-to-FW400 to plug in audio-interfaces having just FW400. Id refrain from using USB-based audio-interfaces for multi-track recording, but the others opinions might vary.
2. HDD. For the first time, internal large-sized HDD (say, 1-2TB, if we are talking about iMac) might be sufficient, but the information grows fast and eats up all the space, yet the reliability of modern disks is so-so. Id recommend thinking about external drives for storing your projects and backups before the thunder comes in town. If for backups only, then any disk having USB2.0 or FW800 connector will fit. If you prefer to record to external drives, youll need to pay more money to get RAID-based ones connected via FW800. With the last option, you might want to consider a MacBook Pro as a mobile alternative to iMac. Personally, I use MacBook Pro for the most of time (moved from old iMac).
3. UPS. Having a lot of disk space powered on along with your computer must be protected on power line use uninterruptible power supplies. This is very important.
4. One of the programs doing multi-track recording. Logic, ProTools, Live, Cubase, etc, it doesnt matter. The level of your confidence and personal preference only matters. The mentioned programs take a lot of RAM when loading large projects, so the more memory you have, the better.