Your uses are at both ends of the PC scale. For a bit of word processing/surfing plus a bit of coding you could use a smelly old P1 / P2 system quite happily, wouldn't be worth buying a new pc if you still have one.
Video editing, differnt kettle of fish. One of the most power hungry things you could ever ask you PC to do. You could have a dual 3GHz p4 with 2 Gig of memory and you'd still think it was too slow.
Basically you're going to have to compromise unless money is no object. An AMD based system is almost always going to be a bit cheaper just due to the cost of thh chips. But for Video work, Intel are probably the best by a nose, but the AMD will do it too. But you might be able to affors a faster AMD chip than and Intel chip so that might level the playing field.
Get as much memory as you can afford. DDR3200 matches well with the newer AMD chips. Without going into the nitty gritty the Barton chips are an improvement on the existing XP chips, I have an XP Barton 3000+, I can only state that it is faster than the P4 1.7GHz and 2.0GHz machines I use at work. DDR3200 is only a little more expensive than DDR2700, I doubt there is a huge difference. If you can't afford 1G of memory get 512 you can always add more later, make sure what you get is on one stick so it doesn't use up all your slots.
Video cards, we use a Radeon 9700 here on a machine for video work and it works well, I'm told. You will have to think what software you want to edit with. XP come with a basic package for editing video but you would probably outgrow that quickly. Adobe Premier is one of the bes products but is very expensive. What about one of the Pinnacle cards, these are specific digital video capture cards and come with (I'm told) good software bundled. The prices for the basic models are not bad.
XP/XPpro, pro is enable for proper networking for larger offices. If this is a home PC stick to home version not worthe the extra. It will still network to other machines in a p2p network.