If you have a Core Duo Mini, then you already have a very good processor. The 1.66 Ghz Core Duo ships in many laptops, even high-end ones. Although laptops are not exactly very good game machines (except for Dell's Inspiron XPS, Alienware & Voodoo laptops, and maybe a few others), a dual-core 1.66 Ghz Intel Core processor really isn't bad, and should compare well to a 2.8-3.2 Ghz Pentium 4 for most tasks (and outperform the P4 with thread-aware apps, thanks to its two cores). The Core Solo is not as fast but is still reasonably fast (it should be a bit faster than a similar, 1.5 Ghz Pentium M processor).
However, the Mini features a 2.5-inch, 5400 rpm laptop hard drive, and has Intel's GMA950 integrated graphics. If you want a better game machine, I suggest you get one with a dedicated graphics card, and a desktop drive (3.5", 7200 rpm) would also improve performance.
If you have the stock 512 MB of RAM, then you will probably notice a significant difference in speed if you upgrade to 1 or 2 GB, especially with intensive applications like games. However, integrated graphics will probably remain the great weakness of the Intel Minis & MacBooks when it comes to gaming.
If you want to play games, and can afford a better computer (and can still return the Mini - should be OK if bought within 14 days, although there may be a re-stocking fee), I advise you to get an iMac, whith 1 or 2 GB of RAM and the 256 MB graphics card option. This one should perform very well, and should also be able to run popular Windows games in Boot Camp ...