So I'm heading off to college in a couple of months and thought it would be appropriate to build myself another computer because my current one is outdated. I'm hoping that this build will help me get through the next 4 years hopefully.
Graphics Card = XFX HD587XZNDC Radeon HD 5870 XXX Edition Video Card - 1GB GDDR5,
Have a look at the sticky at the top of the forum, the one about asking for build advice.
Before we can say what you need, we have to know how you will use it. You don't need that much power for your build as listed, a good PSU with about 40 amps 12V would do just fine.... possibly 50 amps if the card and your CPU will be overclocked.
If you want a small case you should get a smaller MB, then you can get something lighter and easier to fit in small spaces.
Due to the Ripjaw no longer being free shipping, the ECO actually works out cheaper instead of more expensive which is was previously. You do not need more than 4gb of RAM for gaming, I doubt you will need more RAM at all before the time you replace the system, but if you ever do feel the need you can always pick up a few more gb in the future, by the time you feel the need for more DDR3 RAM will be cheaper
In addition to being cheaper it is the best performing HDD.
I cannot help with case as I do not like to go with micro boards or small cases - personally I think a typical sized mid tower is easy enough to carry - they aren't heavy and I have long arms so carrying is easy enough, so the usual HAF 922 type case would be my recommendation
Also, given that you have gone with a great mobo which allows XFire, if ever you decide to do it you want a case that can handle 2 5870s inside it without them being crammed in.
750W is plenty and allows you to XFire in the future if you choose to. Also, if it is the PSU I am thinking of it has a good deal on Newegg so worth getting. No need for 850W, 750W is more than enough for your system and XFire