I did some searching and found this (http://reviews.cnet.com/8301-13727_7-20020233-263.html):
As with all of Apple's new software, iLife '11 requires a Mac with an
Intel processor. iLife '11 is also only compatible with Mac OS X
10.6.3 or newer (the current version is 10.6.4). Your machine must also have at least 1GB RAM and about 5GB of available disk space
(though it is recommended that users retain at least 10 percent of
their hard drive space and leave it open).
A DVD drive is required for installation, and users must have a
minimum screen resolution of 1,280 x 768 pixels.
Some features of iLife '11 require greater minimum specifications.
GarageBand "Learn to Play" requires a Mac with an Intel Core 2 Duo or
better processor. 24-bit recording in GarageBand requires a 24-bit
audio interface that works with Mac OS X.
So I guess I will go for a Mac Mini with at least a Intel Core 2 Duo.