Hi: after suggestions below I will keep quiet...
I think that
before you go out and spend any money on upgrades etc. some things should be done.
1. Run an app like onyx, or cocktail. They will check your drive out, clean/delete all the garbage, handle the permission issues etc.
2. Run the app from the NOVA bench site
http://novabench.com this app will run a series of tests and should tell you if the Mac-mini meets the specs that you paid for. It will/may also show you any specific problem areas.
If machine works as it should then run some tests to see if you still have the performance problem ??? (remember you cleaned out the garbage etc)
If the problem persists then rebuild the entire system. Check to see if all the apps are compatible with your OSx. Upgrade/download every app one at a time then test it. Then the next one, then again.......and again one at a time until you hit the culprit.... Run safari and chrome last keep network apps until the end.
allways try to download and test apple products first.
If you still have a problem and can not find it go the guru at the apple store . Your machine is still under warranty. Maybe he can find it. (unfortunately he does not have access to your network/router leaving out a potential problem area.
cheers Elo.....
this is plain boring work.
have I done this before... yes back in the dark ages..