Here is what I believe you have.
Late 2009 Mac Mini 3,1 ( w/2.26 Ghz Core 2 Duo (P7750) CPU. You also likely have the Nvidia GEforce 9400M GPU with either 128 or 256MB VRAM. Your 2GB (2x1GB) of main memory is 1066 Mhz SDRAM PC3-8500 DDR3 SO DIMMS (204 pin).
Despite what Apple suggests, your 2GB of memory will cause very poor performance with Mountain Lion. I would recommend a single 4GB (1x4GB) memory module, the official maximum, or with the EFI v1.2 firmware update, you could add an additional, single 4GB module for an unofficial 8GB of memory. Do not leave one of those 1GB memory cards in with the 4GB replacement. That 4GB memory module runs between $31.99 and $32.99 here.
There will be a noticeable performance improvement in boot time and operational speed with that additional 4GB memory.
The steps that I previously outlined may also contribute to performance improvements.