If that first link is your PC, then you have a PCI-Express x 16 slot in your motherboard. You also have 3 PCI slots. You will need to purchase a GFX card with 2 connections(today almost every GFX card has 2 connections).
Also, you will need to check the GFX card to see whether it has 2 DVI ports or 1 DVI and 1 VGA. Ur CRT is VGA, and ur 19" may have DVI support. Either way, you could always use 2 VGA connections with a DVI-VGA adapter which often comes with a GFX card.
newegg.com is a good place to purchase cards. You can find a Geforce 6200 for around 35$ which can support dual moniters and will give you improved graphics performace as well. Or you could opt for more expensive cards.