I agree with M733mhz that the performance you'd see between the two speeds of memory would be negligible. That said, if you are moving up from Windows 2000 (or Windows SE or 98) to Windows XP, you may want to consider going to 1 GB of RAM. Windows XP will take up a sizable portion of that 512 MB. Since 667 MHz DDR2 RAM is slightly cheaper than 800 MHz DDR2 RAM, maybe you can swing it.
512 MB of RAM would probably be enough if you were just doing email, browsing the web, and word processing. However, the two apps you want to use - Photoshop and Illustrator - can be incredible memory hogs in their own right. However much RAM you buy, they'll be glad to use it all.
The differences I know of between the E4300 and the E6300 are the the E6300 has Intel Virtualization Technology and a slightly faster front side bus (FSB). Intel Virtualization Technology would most likely never be of concern for you. The faster FSB does give the E6300 a slight edge in benchmarks I've seen. Given that the two prices are similar at least in this case, I'd take the E6300.
Video editing requires a decent CPU and fairly fast disk. Either of those CPUs is up to the task. I would guess that you're looking at a 3.0 Mb/sec SATA hard disk in the new machine, so that should work well. (Especially true given the machine you have now.)
Case: Enermax CS-A106USB
P/S: OCZ OCZ700GXSSLI 700W
Motherboard: ASUS P5N32-E SLI
CPU: Intel E6300(idle 35C/load 39C)
RAM: OCZ Platinum Rev 2 DDR2 800 MHz (4 x 1GB) 4-4-4-15-T1 (2.1v)
Hard Disk: Seagate 2x250GB SATA ST3250620AS in RAID1
Monitor: Mitsubishi DP900u
Graphics: BFG GeForce 8800GT PCI-E
Sound: SoundBlaster X-Fi Fatal1ty
Speakers: Klipsch ProMedia v.2-400 4.1 speakers
Optical: LiteOn 16X DVD-ROM; Sony DRU-710A DVD-RW