Aperture works well with Lion 10.7.5. and it will offer you many advanced features compared to iPhoto.
If you read about problems, they are usually caused by problems on the particular systems running the applications.
I'd check the hardware requirements. How much RAM does your Mac MIni have? Aperture is more efficient with plenty of memory. You should have at least 4GB of memory, more would be better.
Have you looked at the Tutorials at the Aperture Support page? Look at the information there to see, if you would like to work with Aperture, maybe try it out at your local Apple Store?