I'm thinking of getting a mac mini to replace my current crappy acer t650 which can't barely run anything. I don't want to get a imac because I need a computer which can plug into a monitor as I use my monitor for xbox 360 as well as for computer. would the new Mac mini (OS Lion) 2.3GHz dual-core Intel Core i5
4GB memory
500GB hard drive1
Intel HD Graphics 3000

run it? or would the one with AMD Radeon HD 6630M run it better

Please do some research, if you do you will find that the Acer is the worlds second best computer manufactures and mac are the worlds fourth worst manufactures Not only that if you buy a Mac you can't do what you want with it, Mac control everything you do, You own the widget You can't install anything you want on your mac widget, you can only install what mac allow you to install, and you have to buy everything from Mac at high prices,

Let get back to your current crappy acer t650, People always call their computers when things go wrong, They never consider that their computers problem is caused by the operating system, Windows has always had problems and always will have problems, Even with the New windows 8 development release I'm having problems with it crashing and freezing up,

There are free alternative up to date operating systems that you can download and try out, they are faster stable and secure, they don't crash, freeze up or get windows viruses, You can build your own Minecraft server using these alternative operating systems. what I am saying is that the operating system is the major part of a computer, If the operating systems does not work 100% then the computer won't run 100% you will have problems

You can check out the latest November 2011 alternative free operating systems here
http://disrtrowach.com

yup nice rig too. I got good performance in Minecraft with a crappy HP laptop that was 5 years old, and only had a 128 mb integrated card.

Ya your computer is way fast