Gotta disagree with the above, though it depends on the size of the video's you're planning to edit.
My last machine was an Athlon 3200 based machine with 1GB RAM and it took forever to even convert a 1 hour video to DVD format (over 45 mins once it was on the HD) My current rig runs 2GB RAM, a pair of 160GB drives in RAID stripe and a dual core 3.0 P4.
Time to convert now? <18mins
Hard drive speed and processor make the single biggest difference when working with video since the files are so large. If the video's you'll be playing with are sub 15 minute then you can probably get a machine for no more than around the $1000 mark, if you're looking for either professional level video editing, or working with larger video's then expect to be around the 14-1700 mark for a machine that will get the job done.
Also make certain you get Firewire, when trying to bring video over using USB I've found one of two things happen, either a) I get no audio or b) I drop roughly 1 frame of video out of 10 causing the audio to be substantially ahead of the video. Firewire handles large file streaming much better than USB 2.0 does.
For the camera I still use an old Canon ZR65 and found it does fantastic work given my limited skill with the camera. For basic editing/conversion to DVD the software that came with it does great, for more advanced stuff (plus I now convert my old VHS to DVD) I've found Dazzle from Pinnacle studio's to be a reasonable alternative to Adobe's premier.