You don't need a specific graphics card, per se, but you should have a reasonably recent one. I have some older graphics cards that will only handle monitors with a 4:3 pixel ratio but not a 16:9 (or similar widescreen) ratio. That is, they handle monitors with a 1600x1200 resolution just fine, but not those with 1680x1050, which is a typical one for 22" monitors.
I'm sure this is a limitation of the drivers in some cases, but not so in others. Newer cards will handle both and typically come with at least one and often two DVI outputs, which a newer LCD display will also have.
8 MB would (barely) handle the 1680x1050 resolution in 32 bit color, but since any recent card will come with at least 128 MB, that's a moot point. These can be had for under $40. They won't be gaming cards, but for text, 2D video (like playing DVDs), and web browsing, such a card would be fine. You didn't say if you had AGP or PCI-e graphics, but I'd guess the former. Just make sure whatever card you get has the same interface.
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