The original iPad mini has 512mb of ram. I'm not sure what the speed of the ram is but it's decent for most task. My iPad mini came with iOS 6 and it was plenty fast. Crashes were very rare and I could easily have around 5 apps open without one of them closing (depending on the app).
The only times I ran into trouble was when running memory hungry apps like Pages. When creating complicated documents the app would run slow, freaze and then eventually crash. You also may have trouble if you have more than 3 tabs open in safari (depending in the complexity of the website).Overall, the iPad mini is no power house, but it performs good enough for most task.
iOS 7 though is a different story. After updating my mini, the performance dropped considerably. The iPad was still good for most task but the smoothness factor was greatly reduced. I ended up selling my iPad mini a couple weeks after updating. I replaced it with the retina ipad mini and the difference is night and day.
The economy is bad and money is tight for most of us, but if you can afford the extra $100 I would highly suggest going for the retina ipad mini. The retina screen, 1gig of ram and the better processor makes a world of difference, even for the most simple task.