For HD video editing with Premiere, I'd consider a Core i7 processor a minimum requirement and also an Nvidia display card to take advantage of the GPU acceleration. With any video editing machine, you'll also need at least a second fast SATA drive just for video, a single-drive system won't do. Therefore, for video editing, I think that a $1000 max (with display) is unrealistic. You might find a $1000 Core i7 machine at the warehouse club or Dell, etc. but then you still need to add the video drive, possibly more RAM, and most likely a better graphics card and that all adds up.
Not saying you can't use an i5 for instance, but you get what you pay for and performance will be lackluster/frustrating. Do you really need three video editing systems? With the $3000 budget, you'd be better off getting two $1500 machines than three $1000 systems. More productive in my eyes.
Safe Harbor Computers
Have a look at the videoguys.com website as they have some examples of costed DIY systems.
Please do the math on using CC on all the PC's you may find it works out quite expensive after a few years.
If you edit using another piece of software like Edius you can use a far cheaper graphics card.
An alternative to PP and AE in one $299 product is Hitfilm Ultimate.
[Moved to Hardware forum.]
Are you going to edit SD (Standard Definition) or HiDef with Premiere Pro?
If HiDef, $1,000 is not going to get you a computer that is very fast
Buy a Desktop Video Editing PC http://www.adkvideoediting.com/
Build a Desktop Video Editing PC
-3 price level ideas in http://www.pacifier.com/~jtsmith/ADOBE.HTM
-what PC to build http://forums.adobe.com/thread/947698
-2 how to build videos http://forums.adobe.com/thread/1104182
-another video http://forums.adobe.com/thread/1145366
-another video http://forums.adobe.com/thread/1132363
-planning & Building http://ppbm7.com/index.php/intro-part-1
-memory for LGA2011 http://forums.adobe.com/thread/1098759
-an Adobe FAQ http://forums.adobe.com/thread/878520
-several more links http://forums.adobe.com/thread/815798
-build tuning http://ppbm7.com/index.php/final-results
You can only have creative cloud subscription on 2 machines. I would keep it to 2 and build better machines. The illustrator and indesign stuff can be done on just about anything, but for video editing you definitely get what you pay for.
That is just per license. I would agree though that 2 systems that would run CC decently is far better than 4 of the alternative.
Thanks for all the responses. It's really giving good info to think about.
I wish that we could just go with one CC account. Based on the way our tasks are assigned, we have three individuals who would ideal need to have access to the software. But thankfully only two of us will be doing any video editing. I was hoping to have another machine that students/volutneers could use to do creative projects, including video, but maybe that's not so realistic.
Any suggestions on which brands are the best/most reliable/greatest value?
Go back to #5 and the link I posted for ADK to buy ready made
Where to get a good machine? I'd love to give you a quotation, and I'm sure Eric at ADK would oblige you as well ;-)
Seriously, there are a lot of variables involved and buying an off-the-shelf consumer PC is not going to provide the best performance. An Adobe-authorized system integrator will put together the right combination of parts to get you the best performance and reliability for the money, and can also usually install/test the Adobe software as well, to provide a trouble-free experience out of the box. Support is also an important part of the equation. With a big-box computer, don't expect any support with editing issues/workflows, the call center folks overseas will just direct you back to Adobe.
Safe Harbor Computers