By 3D printing software I assume you mean the slicer. Modern machines will have no problem running most slicers. For example Cura has a minimum required hardware of 512 MB of RAM, 200 MB of disk space, Pentium 4 processor and recommended hardware of 2 GB RAM, 500MB disk space and Intel Core 2 - 2.0Ghz.
As always, more power is better and a more powerful machine will allow you to get things done quicker. You can run a 3D printer from pretty much anything now. I have OctoPi running on a Raspberry Pi Model B+ controlling one of my machines and it works really well.
If you’re talking 3D modelling, then that really depends on the software you’re running. You can get away with a fairly low powered machine if you’re using something like Tinkercad or OnShape, but if you want to work with something like Solidworks then you’re going to want the biggest, baddest machine you can get your mitts on.