Running Pro/Engineer is akin to saying 'driving a vehicle'. Are you commuting to the train station or flying to the moon? That decision comes from what you'll be doing with the software. Regardless, I disagree with the poster who put up the specs for a gaming PC.
Since my experience is with Pro, I'll stick to that. You should start with the list PTC puts out for compatible and qualified hardware, especially if this is your day job. You're not going to need state-of-the-art gaming hardware to run Pro/E or Mechanica.
http://www.ptc.com/WCMS/files/71138/en/proewf3.pdf
The cynic in me says if you can afford a legal seat of Pro, you should be able to afford a system > $700 to drive it (unless you're a student with the free version).
If you're doing parts and basic assemblies (< 10 parts), no rendering, you may hit your target. Get a quad core system if you can afford it, dual core if you can't. You'll be fine with 2 GB of RAM and love the x64 XP operating system. Video overhead is the first thing you'll hit, so put your extra money towards that.
If you're starting with much larger assemblies (> 20 parts), then throw more money at RAM, and all of a sudden that IA64 processor starts helping you out.
If you're now onto simulation, complex surface geometries, or FEA -- now's when the processor comes into play. Once loaded, the solid models are really held in graphics and system memory -- only when you start getting fancy with surfaces and the like will you long for a faster processor.
Honestly, if you're worried about cost, remember you can always throttle Pro/E down through config.pro options. Level of detail, absolute accuracy, CPU's to use -- they're all options to tweak.
Last thing I would recommend is a FAST hard drive. Don't skimp here, because no matter how much RAM you put in, Pro still likes to swap to the disk.
Hope that helps -- I've been doing this for a while if you need more advice. Stay away from Vista and Windows 7 like the plague.