Although Premiere Elements will work on most computers sold in the past five years or so, it is definitely to your advantage to have a more powerful system. DV-AVI video files devour huge chunks of hard drive space (at a rate of about a gigabyte of space for every five minutes of video), and the process of capturing, manipulating, effecting, rendering, and outputting those files, particularly on longer projects, can be very processor- (and hard drive space) intensive.
Processors running at more than 1GHz will power the program, but to a limited degree. You might have to shut down background processes in your operating system to capture and output, and rendering larger files can take a frustratingly long time if you're using one of these slower processors. (See 12 About Troubleshooting Capture Problems.)
Most processors running at more than 2GHz should run the program effectively, with 3+GHz Hyper Threading Pentium 4s and Athlon64 3000s and higher having more than adequate power to run all of the program's features. (Note that Premiere Elements works only with Athlons that use the SSE2 instruction set. A BIOS update might be required on some older machines, and pre-XP Athlon chips might not be able to run the program at all.)
Likewise, although 256MB of RAM is the minimum recommended by the program, at least 500MB is highly recommended and 12GB of RAM is ideal.
A large hard drive is also very important, not just because video files are huge but because Premiere Elements requires large amounts of free, contiguous hard drive space to write temp files and to use as scratch disk space. Maxing out a hard drive is something most people don't consider but, especially with larger projects, it happens more often than you'd expect. At least 60GB of free space is recommended for a typical project, although high-demand projects might require more. (See 124 About Troubleshooting DVD Output.)
Scratch disk An area of your hard drive in which Premiere Elements writes temporary files while rendering and encoding your project. Often the amount of scratch disk space needed to render and encode a project exceeds the size of the output file.
Although a second hard drive, one dedicated to your captured video and video temp files, is ideal (and is standard equipment for most professional editors), most desktop computers sold in the past year or two are more than capable of handling the video files and operating system on a single hard drive. However, if you experience data flow problems (such as dropped frames or interrupted capture or output), know that the installation of a second, video-dedicated hard drive often remedies the problem. (See 12 About Troubleshooting Capture Problems.)
Finally, a nice, large monitor is definitely to your advantage when you're editing video. There's a lot going on onscreen, and you can greatly benefit from as much real estate as possible to allow for viewing all your timelines and having ready access to your tools and folders. Although a 17-inch monitor set to 1024768 resolution will give you enough room to see everything, a 19-inch monitor with resolution settings at 1280960 or higher allows you much more room to work. For the truly ambitious, Premiere Elements supports dual monitors so you can place your Monitor panel on one screen and your controls and tools on the other.
Whatever you choose, you'll find that you'll appreciate every pixel of screen space you can afford.