If you are being asked to authenticate it is because of a security feature that is in place on the OS. If you feel ok with logging in then it is ok to use these ports, however these are the same ports as used on live webservers so if you have any security concerns you should use the defaults.
You should be able to control the machine via VNC with the default setup. To enable VNC on the mini go to system preferences > internet and networking > sharing. In here make sure that you have the option for screen share enabled.
Next you need to install a VNC client on the machines you would like to remote into the mini with. If you are on a mac I would suggest Chicken of the VNC, it is a client that I have used and it works well. On a PC you should look for TightVNC, it is a free one.
