What microcomputer is best?

if you're going to be spending $800, don't get a micro computer, you can easily afford a standard ATX form factor computer for that price and it will perform a lot better than any Micro computer:

If you're capable of building your own (it's really not hard), start of with a nice case and a reasonable 600W or so power supple (Corsair, Silverstone, Coolermaster, etc..) and a reasonable motherboard based on the Intel/AMD platform you wish your computer to run on. Get 8GB (2x4GB) RAM to support it, something along the lines of an Nvidia GTX 650, whatver CPU from the range you can afford, and a basic hard drive.

This will give you the foundations for a good PC and over time you will be able to upgrade it as you wish, without wasting the Micro PC

I second Tim Fontana's idea. If you're going to be spending $800, you can build a pretty beastly computer. You seem excited to add RAM, so building a computer would be perfect for you (you can still install RAM in the Mac Mini by the way).

I am able to create a parts list for you if you are interested. In order for me to assemble a parts list, I will need some information:
Would you like Windows to be in the price (you could always run Linux for free!)?
Do you need keyboard, mouse, monitor?
Is the budget flexible (considering you would need a keyboard, mouse, and monitor with either the NUC or Mac Mini)?
What form factor would you like (Most builders choose ATX, but another common form factor is MicroATX)?
Even though many first time builders tend to go for Intel, would you be open to an AMD based CPU for more bang for the buck?

I put this together for you quickly, this would be a very powerful computer, After rebate it would come to just over $740, money with which you could invest in a better cooling system and possibly an optical drive (I've left this out in the original instance since most people have no need for them any more, one can be added for about $20)

This would perform many times better than any micro PC that is on the market and would also be a foundation for any sort of project you wish to start.

The Intel parts (CPU and Motherboard) could be swapped for slightly less expensive AMD parts if you wished to keep your spending a little lower, however, I myself am partial to Intel products and while there are no issues with AMD parts, I prefer not to use them in my computers.

Parts links are here:

Case: http://www.newegg.com/Product/Product.aspx?Item=N82E16811129066

Power Supply: http://www.newegg.com/Product/Product.aspx?Item=N82E16817139005

Motherboard: http://www.newegg.com/Product/Product.aspx?Item=N82E16813131837

Processor: http://www.newegg.com/Product/Product.aspx?Item=N82E16819116504

Memory: http://www.newegg.com/Product/Product.aspx?Item=N82E16820145345

Video Card: http://www.newegg.com/Product/Product.aspx?Item=N82E16814127710

Hard Drive: http://www.newegg.com/Product/Product.aspx?Item=N82E16822148840

I shall also include a link to a good CPU cooler that you could consider if you wished to overclock the CPU a little, but this is not necessary unless you wish to push your system to the limit of what it can do and know a little about what you're doing.

http://www.newegg.com/Product/Product.aspx?Item=N82E16835103065 - This is a good, well priced cooler that performs incredibly well.

Also, please note that I haven't included and operating system in this list, but Windows 7 can be obtained fairly cheaply these days.

Also, the parts I have listed are just ones that I put together quickly, while I am sure that they will all work well together, there may be other parts that do the same job for less money or that you prefer, I am willing to help you chose these parts if you want, my email is tim@fontana.me.uk if ever you wish to discuss this further.#

I hope this has been able to shed a little bit of light on your situation.