Well, a lot depends on the type of video you'll be editing.
But I'd recommend at least an i5 quad-core processor with 4-8 gigs of RAM, an ATI or nVidia graphics card and 500 gigs of hard drive space. Even better if you can install a second drive just for your media files. Virtually all Windows 7, Windows 8 and Mac operating systems are 64-bit now, but I'd ensure this is true too.
Intel processors will give you best performance. But, if you opt to go with another processor, check out this chart and ensure your processor rates at least a 6,000.
I had a computer with an i5, 8 gigs of RAM and 500 gigs of HDD. It worked OK. I used it to learned PrE 9 and 10 with a lot of help from Steve Grisetti and others.
Being an impatient person, I wanted faster and more lively video editing. I want the reder bar to go away quickly and I don't want output encoding to take very long. I found what I wanted in a ASUS "Republic of Gamers" laptop. Yes, they really call it that. Specs include: Intel i7 Quad-Core processor, 16GB RAM, 256GB SSD, 750GB 7200 RPM HDD, nVIDIA Graphics, HD Led-Backlit Display with 1920 x 1080 Native Resolution, a Blu-ray Player and Burner, 4 USB 3.0 Ports (for external backup and storage) and a Card Reader.
When I bought it PrE11 was brand new. I took Steve Grisetti's PrE11 editing class on Lynda.com.
Put all together, I do have a lot of fun with video editing.
Are you planning to buy a desktop, or laptop... and are you going to edit HiDef video?
If you are going to edit HiDef video, especially that from a DSLR camera, you need "somewhat" more than Adobe's minimum specifications
8Gig MINIMUM ram, 16gig might be better
2 7200rpm hard drives, or SSD and 7200rpm hard drive (as already mentioned)
ATI graphic card with at least 512Meg ram (1)
Read computer specifications to find one with Firewire... or, if a desktop, buy a Fireware card that uses a TI chip http://forums.adobe.com/thread/940242
(1) Premiere Elements does not use the GPU for hardware acceleration like Premiere Pro, so a more expensive nVidia card is not really needed... minimum 512meg video ram, 1Gig of video ram if you are also going to use Photoshop for large pictures
I will build a desktop. I think I will go for an i7 CPU, 16GB, one SSD and one HDD
Any recommendation regarding display vendor/type?