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If you have a 2011 Mac Mini as you signature shows, then it will run it. I'm running Mountain Lion on a 2009 mini.
 
Thanks. I have 4GB, should be ok??

Do I install over, or full new install??
You can never have too much RAM.

Installing over is fine. There is no point erasing and installing if you then intend to Migrate all your user data, settings and apps over.
If you want to spend hours selectively restoring everything by hand, then yes, do a clean install. :p
 
"Thanks. I have 4GB, should be ok??
Do I install over, or full new install??"

I've got a 2012 Mini with ML, and 4gb of RAM is doing fine for what I need (your needs may be different).

If you have a way to completely backup the internal drive (I'd suggest a bootable clone created with either CarbonCopyCloner or SuperDuper), I'd suggest
- backup to external
- boot from external
- re-initialize internal drive
- install new OS
- migrate old account and data files over with migration assistant

That's how I'd do it, others might suggest different approaches.
 
- re-initialize internal drive
- install new OS
- migrate old account and data files over with migration assistant
All this does is puts a new OS onto a clean disk, after which you then replace everything else that was on there.

A default installation simply replaces the old OS with a new one, leaving everything in place.
So the net result is the same, +/- excessive unnecessary wear on the disk.

Most problems are likely to come from user settings and preferences, rather than actual system files. So either way: leaving them there, or migrating them all back, there's no difference.
 
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