There a countless ways to run Windows software on Mac, but first of all you might want to look at alternatives to your software that work on Mac. If you can't find any good ones, i've listed some ways to run Windows software on Mac, starting with the easiest first:
1. Emulation. This is a good choice for those who aren't very tech savvy, but only around 40% of Windows software will work and it is quite expensive. If you want to do this - which isn't the best choice - you can use Crossover for Mac, which has a big support team behind it.
2, Virtualisation. You can install Windows in a virtual machine on software like VirtualBox, Parallels or VMware. This is okay, but only if you have a quite a high-end Mac, which a Mac mini isn't really. This is also quite unreliable because drivers often don't work and programs that need a graphics card will refuse to work.
3. Dual-booting. You can install Windows on a partiton of your computers hard-drive or SSD. This is basically guaranteed to work with all Windows software, provided you have a high enough version of Windows and your computer meets the system requirements. You can dual-boot windows using your Mac's built-in Boot Camp Assistant. It helps to know a bit about computing before you try this though, and make sure you have an external hard drive to back up your data beforehand.
4. Porting. This is perhaps the most convenient method, but requires a lot of technical knowhow which I myself don't completely have. An application called 'Wine' is used to port applications. Some applications are really easy to port yourself and some already have ports made for them anyway, but if they don't have ports and won't work straight away, you're stuck.
Now, all HDMI monitors will work with Mac mini and essentially any Windows USB 2 or 3 keyboard will work on Mac; no questions asked. If you need further indepth help, you should consider directly contacting apple.